We developed a front-end ASIC for future PET scanners with Time-Of-Flight (TOF) capability to be coupled with 4×4 Multi-Pixel Photon Counter (MPPC) arrays. The ASIC is designed based on the open-IP project proposed by JAXA and realized in TSMC 0.35μm CMOS technology. The circuit comprises 16-channel, low impedance current conveyors for effectively acquiring fast MPPC signals. For precise measurement of the coincidence timing of 511-keV gamma rays, the leading-edge method was used to discriminate the signals. We first tested the time response of the ASIC by illuminating each channel of a MPPC array device 3×3mm2 in size with a Pico-second Light Pulsar with a light emission peak of 655nm and pulse duration of 54ps (FWHM). We obtained 105ps (FWHM) on average for each channel in time jitter measurements. Moreover, we compensated for the time lag of each channel with inner delay circuits and succeeded in suppressing about a 700-ps lag to only 15ps. This paper reports TOF measurements using back-to-back 511-keV signals, and suggests that the ASIC can be a promising device for future TOF-PET scanners based on the MPPC array.