The present invention relates to an acrylic pressure-sensitive adhesive composition containing an acrylic polymer and a tackifier obtained by acid modification of a tackifier resin inherently free of an acid component; a pressure-sensitive adhesive tape including a substrate made of a film comprising an olefin polymer or a thermoplastic resin containing a carbonyl oxygen atom in the molecular skeleton, and the acrylic pressure-sensitive adhesive composition on at least one surface of the substrate, and the like. The invention provides an acrylic pressure-sensitive adhesive composition having high adhesive strength (particularly initial adhesive strength) to an adherend having lower polarity, such as an olefin polymer heretofore been considered poorly adhesive, wherein degradation of the adhesive strength after heating and preservation has been suppressed, as well as a pressure-sensitive adhesive tape comprising the composition. The pressure-sensitive adhesive tape of the present invention is also useful for binding.