Using pulse trigger signal to generate non-equilibrium carriers in semiconductor, a method for minority carrier lifetime mapping of semiconductor was proposed, with the aid of a terahertz continuous wave source and an ultrafast-response probe, which can apply for characterizing transient carrier dynamics in semiconductor. Based on the above-mentioned design principles, a non-contact minority carrier lifetime measuring system was set up by using the optical pump as the periodic excitation, whose time window was from nanosecond to second and temporal resolution was the order of nanosecond. The system owned various advantages, such as simple device, convenient operation and low cost. The non-equilibrium minority carrier lifetime of monocrystalline silicon with different doping types, different doping concentration, and different thickness were measured by using our system. Finally, the photo-generated carrier lifetime of the monocrystalline silicon was measured through changing the optical pump power. Result shows that the minority carrier lifetime of monocrystalline silicon increases with the enhancement of pump power. The wide-working-window and high-time-resolution detection of terahertz fast processes, which is realized by the proposed system, can be applied for the fast imaging and rapid bio-response detection at the terahertz range.