"The mobilisation on the 31st is not to ask anything of the government, nor is it a protest. It is to say that in 2015 there will be a government of the people," Podemos leader Pablo Iglesias told a news conference.
Spain will hold regional and municipal elections in May and a general election is expected in November.
Even though it was only founded in January 2014 several polls have shown Podemos, with its pledge to defend the poor and bring to heel the elite "caste" of politicians and bankers that rule the country, tops voting intentions.
The most recent survey published on Sunday in top-selling daily newspaper El Pais puts support for the party at 28.2 percent, ahead of the main opposition Socialists and the ruling conservative Popular Party which came third.
"Just like on December 31st when we say goodbye to the year that has just ended, we hope that this march for change will allow us to say goodbye to the caste," said Iglesias.
The 36-year-old pony-tailed political science professor would not set an objective for the number of participants, saying only that Podemos wants to "fill" Madrid's central Puerta del Sol square.
"We want a historic mobilisation, we want people to be able tell their children and grandchildren 'I was at the march for change' that opened a new cycle of political change in Spain," he added.
Podemos, which is often accused of populism by its adversaries, won 1.2 million votes and five seats in the elections for the European parliament in May 2014.
It was born out of the "Indignants" protest movement that filled Spanish streets and squares in mass demonstrations from 2011 in anger at the political system, fanned by an economic downturn that has left nearly one in four out of work.