A process for producing a modified particle, a carrier or a catalyst component for addition polymerization, which comprises the steps of (1) contacting a compound (a) represented by the defined formula M.sup.1L.sup.1.sub.3 with a compound (b) represented by the defined formula R.sup.1.sub.t-1TH, thereby producing a contact product, and (2) contacting the contact product with a porous particle (d) and then with a compound (c) represented by the defined formula R.sup.2.sub.t-2TH.sub.2; a process for producing a pre-polymerized catalyst component or a catalyst for addition polymerization, which comprises the steps of (1) contacting the above modified particle with a transition metal compound and optionally an organoaluminum compound, thereby producing a primary catalyst, and (2) pre-polymerizing an olefin in the presence of the primary catalyst; a process for producing a catalyst for addition polymerization, which comprises the step of contacting the above catalyst component with a transition metal compound and optionally an organoaluminum compound; and a process for producing an addition polymer, which comprises the step of addition polymerizing an addition polymerizable monomer in the presence of the above catalyst.