[Problem to be solved]There is provided a process for producing an olefin polymer that is capable of producing an olefin polymer having high heat resistance and high molecular weight with excellent catalytic activity.[Solution to problem]The process for producing an olefin polymer includes a step of polymerizing at least one olefin selected from ethylene and α-olefins having 4 to 30 carbon atoms in the presence of an olefin polymerization catalyst containing a transition metal compound represented by the general formula [I], the olefin polymer including constituent units derived from ethylene and α-olefins having 4 to 30 carbon atoms in a total amount between more than 50 mol % and not more than 100 mol %, [in the formula [I], R1, R3 and R5 to R16 are each independently a hydrogen atom, a hydrocarbon group or the like; R2 is a hydrocarbon group or the like; R4 is a hydrogen atom; M is a transition metal of Group IV; Q is a halogen atom or the like; and j is an integer of 1 to 4].