Abstract: Disclosed are a propylene polymer having a high crystallinity of a boiled heptane-insoluble component contained therein, a high stereoregularity and an extremely long mesochain (continuous propylene units wherein directions of {acute over (&agr;)}-methyl carbons are the same as each other), and a process for preparing said polymer. Further disclosed is a propylene polymer composition comprising the above propylene polymer and at least one stabilizer selected from a phenol type stabilizer, an organophosphite type stabilizer, a thioether type stabilizer, a hindered amine type stabilizer a metallic salt of higher aliphatic acid. The propylene block polymer of the invention is well-balanced between rigidity, heat resistance and moisture resistance, and can be favorably used for sheet, filament, injection molded product, blow molded product, etc.