Scientific computing plays a key role in laser fusion research. In China, much effort has been paid over many years to develop 2D and 3D computer simulation codes, forming a 2D simulation capability through which the key physics issues of laser fusion can be individually simulated, mainly using the LARED code family containing six different 2D (and partially 3D) code series. The main physical processes and the characteristics of laser fusion, and the necessary scientific computing requirements are first reviewed. Then the main functions of the LARED code series and some of their applications in laser fusion research are given. A roadmap to develop a new generation of high performance codes for the full simulation of indirect drive laser fusion is presented. Finally, some challenging problems in laser fusion computing are discussed.