The applicants are seeking a declaratory order that the president has failed to diligently consider and decide on their applications for presidential pardon.
They also want the court to order the president to consider and decide their applications within a month of the court's order.
The court bid follows the Constitutional Court's ruling last September that the president - and not the justice minister - should be held accountable for the delay.
Mqabukeni Chonco and 383 others had initially sued the justice minister for the delayed pardons.
However, the court found "the president retains full powers and functions and is therefore the bearer of all obligations in the greater pardons process".
The IFP, of which Chonco and the other applicants are members, then decided to institute legal action against Zuma.
Chonco was convicted of murder in the late 1980s and was sentenced to life in prison.
He applied in 2003 to be pardoned by the president for his crime.
Chonco claimed the murder for which he was convicted was committed for a political motive.
He did not participate in the Truth and Reconciliation Commission's amnesty process because the IFP did not participate in the proceedings.
The party had instructed him not to apply for amnesty.
In the course of 2003 he was joined by 383 applicants seeking pardon on the same grounds. - Sapa