Fast timing capability in X-ray observation of astrophysical objects is one of the key properties for the ASTRO-H (Hitomi) mission. Absolute timing accuracies of 350 micro second or 35 micro second are required to achieve nominal scientific goals or to study fast variabilities of specific sources. The satellite carries a GPS receiver to obtain accurate time information, which is distributed from the central onboard computer through the large and complex SpaceWire network. The details on the time system on the hardware and software design are described. In the distribution of the time information, the propagation delays and jitters affect the timing accuracy. Six other items identified within the timing system will also contribute to absolute time error. These error items have been measured and checked on ground to ensure the time error budgets meet the mission requirements. The overall timing performance in combination with hardware performance, software algorithm, and the orbital determination accuracies, etc, under nominal conditions satisfies the mission requirements of 35 micro second. This work demonstrates key points for space-use instruments in hardware and software designs and calibration measurements for fine timing accuracy on the order of microseconds for mid-sized satellites using the SpaceWire (IEEE1355) network.