To obtain a norbornene-based addition polymer in a high activity by performing an addition (corpolymerization of a norbornene-based monomer, etc., in the presence of a catalyst consisting of a specific transition metal compound and a specific co-catalyst.

This method for producing a norbornene-based polymer is provided by performing an addition (co)polymerization of (A) a norbornene-based monomer with (B) a monomer copolymerizable with the component (A) as necessary, in the presence of (C) a catalyst consisting of (a) a transition metal compound belonging to the group IV in the Periodic Table containing a cyclopentadienyl group having one or more substituent containing a polar group with (b) a co-catalyst selected from (i) an organic aluminum compound (e.g.; methylaluminoxane), (ii) an ionic compound capable of producing a cationic transition metal compound by reacting with the component (a) [e.g.; trityltetra(pentafluorophenyl) borate], (iii) a lewis acid compound (e.g. triphenylboron) capable of producing a cationic transition metal compound by reacting with the component (a).