Transient photocurrent in hydrogenated amorphous silicon is studied in all relevant time regimes following the illumination of a pulse of light at one end of the sample. When both electron and hole transport are taken into consideration, we find that, at a low occupation level of trap states or at a low intensity of illumination, there are five well-defined current slopes. The first three are located at a short-time range, which has not been probed experimentally, and they are due to the electron transport. The last two slopes originate from the well-known phenomenon of hole transport. Each bend from a current slope change has a particular physical meaning and is interpreted. At a high illumination intensity, all five current slopes become less well-defined, and the two current slopes that are due to hole transport can change drastically because of significant space-charge effects. In particular, one of the hole slopes can even change from negative to positive, and the result is quite different from the well-known dispersive transport theory in disordered semiconductors.