We investigate the dephasing of excitons in InAs self-assembled quantum dots by using a transient four-wave-mixing technique. A used sample is specially designed to compensate the strain. We observe long-lived coherence of excitons at 5 K which corresponds to the dephasing time longer than a nanosecond, where the photon energy of the excitation pulse is 0.874 eV. We find that a pure dephasing due to exciton-phonon interactions dominates in the exciton dephasing rather than the population decay and the exciton-exciton interaction in the weak excitation region, by analyzing the population lifetime and the polarization-dependent dephasing time. quantum dot, strain compensation, dephasing, four-wave mixing, population lifetime, optical anisotropy.