We have developed a PET detector module based on sub-millimeter lutetium oxyorthosilicate (LSO) crystal block and prototype Silicon Photomultiplier (SiPM) arrays with additional fast timing output. The LSO array consists of 20×20 crystals of which each pixel is 0.78 × 0.78×3 mm3 and the pitch is 0.8 mm due to the reflector between pixels. The FM SiPM array and FB SiPM array are arranged 4×4 with 4×4mm2 size for each pixel and 0.2mm gap between adjacent pixels. Through dual readout of both fast and standard output signals from this new SiPM, good energy and timing performance can be achieved at the same time. Through multiplexing and summing scheme and charge division resistor network, sixteen channels of fast output and sixteen channels of standard output are reduced to one fast timing signal and four energy signals, making the detector block compact and scalable in building PET scanners. The performance of FM and FB detector module was evaluated. 16×16 LSO crystals were resolved in the flood image and the edge crystals could be identified if a light guide was used. The average energy resolution of FM detector and FB detector were 15.3% ±1.4% and 11.3% ± 0.7%,respectively, at 511 KeV. Through time pick-off method of leading edge discriminator (LED), the average coincidence resolving timing (CRT) of the block against a 3x3x20mm3 coupled with a FB30035 pixel were 401± 10 ps for FM detector and 303 ± 16 ps for FB detector. The average block-to-block CRT were estimated to be 495 ps for FM detector and 324 ps for FB detector. The FB array has demonstrated a better performance due to its much higher PDE at 420nm wavelength than FM array. We conclude that the proposed design is feasible for developing sub-millimeter resolution TOF PET detectors.