In this paper, we exploit the uplink radio resource allocation considering proportional fairness among users in heterogeneous wireless networks. Meanwhile, multi-mode user terminals are assumed to have the capability of using multiple radio access technologies simultaneously. To this end, a joint optimization problem is formulated for power and bandwidth allocation for uplink transmission. Since the formulated primal problem is difficult to solve directly, we make continuous relaxation and obtain a near-optimal solution using Karush-Kuhn-Tucker conditions, and then propose a joint resource allocation algorithm. Simulation results show the proposed algorithm work, and the algorithm provides superior system throughput and much better fairness among users comparing to a heuristic algorith