There are disclosed: (1) a process for producing a catalyst for ethylene polymerization, which comprises the step of contacting with one another: (i) a solid catalyst component containing at least titanium, magnesium and halogen atoms; (ii) an organoaluminum compound; and (iii) a heterocyclic compound; and (2) a process for producing an ethylene polymer, which comprises the step of polymerizing ethylene, or ethylene and at least one kind of an addition polymerizable comonomer other than ethylene, in the presence of the above-mentioned catalyst.