A terminally-modified polybranched polyimide which can be efficiently complexed with an inorganic material is obtained by reacting a component (a): tetracarboxylic dianhydride; a component (b): as an amine component, a mixture of a triamine and a diamine (which may be composed of a triamine only); and a component (c): as a terminal component, a compound selected from general formulae (1-1) to (1-4). H2N—X—R1  (1-1) (In the formula, X represents a single bond or an alkylene group having 1 to 3 carbon atoms, and R1 represents a nitrogen-containing heterocyclic group). H2N—X—R1  (1-2) (In the formula, X is as defined above, and R1 represents a sulfur-containing heterocyclic group or an aryl group having a thiol or thioether group in the molecule.) (In the formula, R represents a nitrogen-containing heterocyclic group.) (In the formula, R represents a monovalent residue.)