A quasi-optimum fuel assembly allocation scheme for boiling water reactors was proposed and confirmed. It is characteristic of the scheme that the criteria function is represented by fuel assembly allotment to fuel groups. For each fuel group, a required property is given beforehand, and fuel assemblies are allocated to the core to determine the group property as closely as possible. By using the scheme, a fuel assembly allocation is obtained that has a large cycle burnup within a restriction for the peak-to-average power ratio. Another allocation is obtained that results in a large burnup of discharged fuel using a different criteria function. However, it is impossible to obtain a strictly optimum solution for a given criteria function because of the vast number of possible fuel assembly allocations. The search range is reduced by adopting a two-step scheme. In the first step, an optimum allocation of fresh fuel assemblies is searched for, based on proper criteria. Then, in the second step, without moving the fresh fuel assemblies, an allocation of reload fuel assemblies is determined that ascertains the required group property as closely as possible. Results of the numerical calculation show that the scheme is very useful for practical fuel assembly allocation.