An apparatus for controlling a compressor includes: an operation information detector which detects operation information from various sensors according to an operation of a vehicle; a compressor which compresses a refrigerant for operating an air conditioner; and a controller which performs starting acceleration control of momentarily decreasing an operation rate of the compressor, which uses engine power in an acceleration situation of the vehicle, in which the controller stores a first map, in which a starting acceleration entry condition according to a driving pattern and a heat load of the vehicle is defined in a plurality of levels, sets a starting acceleration entry condition having a final level corresponding to the driving pattern according to a starting acceleration entry frequency of a driver for a predetermined unit time within a limited level range of the first map, and adjusts a starting acceleration control frequency of the compressor.