An algorithm for computing electron repulsion integrals (ERIs) oriented to the general contraction scheme is presented. The accompanying coordinate expansion (ACE) method of Ishida is utilized to derive an efficient algorithm. The performance estimated with the floating-point operation (FLOP) count is about N2 times and more as efficient as the conventional algorithm for the segmented contraction scheme, where N indicates the number of contracted Gaussian-type orbitals (GTOs) contained in a set of generally contracted GTOs. The efficiency is also confirmed by using a realistic molecular system, the benzene molecule, with C:14s9p/3s2p, H:8s4p/2s1p, and C:14s9p/6s5p, H:8s4p/4s3p basis sets. The measured central processing unit (CPU) time is in good agreement with the FLOP count estimation.