For the safety and the control of a nuclear power plant it is necessary to simulate the constituent processes on a computer system. The three-dimensional multigroup neutron diffusion equations are commonly used to describe the nuclear fission in the reactor core. They form a complicated system of coupled parabolic partial differential equations (PDEs) whose solution can involve very intensive computing. In this paper this system of PDEs is discretised using a special cell-centred mixed finite volume method (NEM-M0) in space, and a method that combines Crank-Nicholson and the BDF(2)-method in time. The linear equation systems which arise are solved with Multi-Grid as well as with preconditioned BiCGStab. The kernel of both solution methods is an effective Block-SOR method that makes use of the particular structure of the linear equation systems. The parallelisation strategy is based on a grid partitioning that distributes the data and the work homogeneously on the processors. Finally the program was tested for three typical reactor simulation problems on grids with differing coarseness. The speedup achieved by parallelising Multi-Grid and preconditioned Bi-CGStab was outstanding for all examples; even superlinear in some cases. Moreover, the parallel execution times were better than the parallel execution times of other established reactor simulation codes.