Abstract: Radiation pulse shaping for indirect-drive laser fusion ignition targets was studied in detail with numerical simulation. A four-step pulse was shaped first, according to the description of Lindl about low-entropy compression of DT fuel, requiring that the DT ice is compressed by four shocks that coalesce near the inside surface of the fuel. But the fuel entropy is quite high driven with this pulse. The causation is that an additional strong shock is produced during the acceleration phase. Then a new pulse was shaped to compress the fuel well. It includes three steps and rises to top temperature by two slopes. This pulse changed the time and the pressure of the fourth shock, which could effectively avoid the production of the additional strong shock. The entropy increase which happens because of terminating the pulse too early in order not to ablate the ablator too much is also described in this work. The new pulse presented here resolves this problem well by controlling the time when the pulse reaches the top temperature.