We report on the development of versatile APD-based PET modules with time-of-flight capability. The module consists of a LYSO matrix optically coupled with a position-sensitive avalanche photodiode (APD) array, and front-end circuits (FEC) directly connected to the rear-end of the APD package. Each APD device has a monolithic 16x16 (or 8x8) pixel structure with an active area of 1.0 (or 4.0) mm2 for each pixel. Time resolutions of 155 ps and 214 ps (FWHM) were obtained for 1.0 mm2 and 4.0 mm2 APD pixels, respectively, measured by the direct detection of 10 keV X-rays. The FEC carries two identical analog ASICs specifically designed for the APDs in TSMC 0.35 μm CMOS technology. Each ASIC consists of 32-channel charge-sensitive amplifiers, band-pass filters, differentiators, pulse-height and timing discriminators, and two-channel time-to-amplitude converters. The noise characteristic of the ASIC, mounted in a low temperature co-fired ceramics (LTCC) package, is 560 +30 e-/pF with an electric timing resolution of 484 ps (rms). The overall dimension of the module (including APD-array, LYSO matrix and FEC) is 30x30x80 mm3. The variation of signal amplitude was less than 20% among all pixels. The average energy resolutions of 11.7 ± 0.7 % and 13.7 ± 1.1 % were obtained for 662 keV gamma-rays, measured with 8x8 and 16x16 arrays, respectively. An attainable spatial resolution is < 0.8mm (FWHM) for 16x16 array in a reconstructed image. These results suggest the APD-based PET module can be a promising device for future applications, especially for high resolution MRI- and TOF-PET.