In the process of the present invention, a solvent-soluble polyimide is produced by polycondensing at least one tetracarboxylic acid component with at least one diamine component in a solvent in the presence of a tertiary amine. The tetracarboxylic acid component is selected from the group consisting of tetracarboxylic dianhydrides represented by the following formula 1: ##STR00001## wherein R is as defined in the specification, and tetracarboxylic acids and their derivatives represented by the following formula 2: ##STR00002## wherein R and Y.sup.1 to Y.sup.4 are as defined in the specification. Unlike the conventional techniques using an excessively large amount of a chemical imidation agent such as acetic anhydride and a chemical imidation catalyst such as triethylamine, in the process of the present invention, the solvent-soluble polyimide having a high polymerization degree is easily produced in a solvent with good productivity by using only a catalytic amount of the tertiary amine.