This paper proposes a rate allocation scheme for throughput maximization considering rate fairness in wireless relay systems. The throughput maximization problem is formulated to two link data rate balancing problems: global balancing and local balancing. And the rate fairness is converted to data rate balancing of each destinations. Based on this, we construct a feasible rate region (FRR) which is the set of achievable data rates. Since FRR is a polyhedra, rate allocation is performed by searching the intersection points of FRR. In addition, if the system is infeasible, the proposed rate allocation removes the destination for system feasibility. Simulation results reveal that the proposed rate allocation maximizes the throughput with satisfying rate fairness, not only for the feasible case but also for the infeasible case.