A sea of demonstrators chanted "Yes we can!" and carried signs reading "The change is now" as they made their way from Madrid city hall to the central Puerta del Sol square in the first major march called by Podemos, which has surged ahead in opinion polls in a crucial election year.
Many in the crowd also waved Greek flags and the red and white flags of Syriza, an equally radical party whose stunning win at the polls last week has buoyed Podemos and its anti-establishment message.
"The wind of change is starting to blow in Europe," Podemos leader Pablo Iglesias, a pony-tailed former university professor, said in Greek and Spanish as he addressed supporters at the so-called "March for Change". "We dream but we take our dream seriously. More has been done in Greece in six days than many governments did in years," the 36-year-old said.
Syriza beat mainstream Greek parties with vows to end painful austerity measures and corruption and Podemos hopes to emulate its success with a similar message in Spain's general election due in November.
Organisers put the turnout in Madrid at 300,000 while police said some 100,000 people had massed in the Spanish capital.
Podemos, which means "We Can", was formed only a year ago but the upstart party already shook up the political scene last May by winning five seats in elections for the European Parliament.
Born out of the "Indignants" protest movement that filled Spanish squares in 2011 with demands for political change, Podemos says it wants to prevent profitable companies from firing people, promote a fully state-controlled healthcare system and enact a "significant" minimum-wage hike.
The party has struck a chord with Spaniards enraged by a string of corruption scandals, as well as public spending cuts imposed by the conservative ruling party and previously by the Socialists after the economic crisis erupted in 2008.
"There are many people that agree with the need for change. Enough already with stealing -- that the corrupt take everything and we can't do anything," said Dori Sanchez, 23, an unemployed teacher who came from Monover in southeastern Spain for the rally.
Podemos said 260 buses brought supporters to Madrid from across Spain, while hundreds of locals signed up to host travellers.
"I want real change, that they stop fooling us," said Blanca Salazar, 53, a geriatric aide who travelled from the northern city of Bilbao with her husband and nephews.
Spain has now officially exited recession -- the country's economy grew by 1.4 percent last year, according to provisional data released Friday -- but nearly one in four workers is still unemployed. Salaries for many people have dropped and the number of workers on low-paid short-term contracts has soared.
Podemos has overtaken the main opposition Socialist Party in several opinion polls, and in some has topped the list ahead of the conservative ruling People's Party (PP). The Socialists and the PP have ruled Spain alternately since the country returned to democracy after the death of the dictator Francisco Franco in 1975.
Prime Minister Mariano Rajoy has warned Spaniards not to "play Russian roulette" by supporting Podemos, which he said "promises the moon and the sun" but will not deliver. Speaking in Barcelona as the rally was taking place, Rajoy said radicalism was "unfortunately very much in fashion in our country" without mentioning
"I don't accept the gloomy Spain which some want to portray because they think that by doing so they will replace those who are governing and have had to face the most difficult crisis in decades. They will not succeed," he added.
Critics of Podemos have accused it of having links to Venezuela's left-wing leaders and alleged fiscal irregularities by some of its top members. The party's leaders have promised to publish their tax returns to dispel the allegations.