In this paper, a new radio resource allocation approach for mobile data offloading, by means of a local access point (LAP) in the heterogeneous cellular networks is proposed. We consider the uplink path in a single‐carrier frequency‐division multiple access–based multiuser system in a 2‐tier cellular network with a macro base station (BS) and set of LAPs. We assume that there is no internetwork interference between macro BS and LAPs due to the use of 2 different sets of frequencies. Our aim is to allocate resources to determine the best strategy for providing the required quality of service with the criterion of minimum delay in terms of effective capacity maximization. The basis of this work is optimization for the strategy selection. In other words, the selection of the best station and power allocation for offloading in a single‐carrier frequency‐division multiple access multiuser system and solving the problems using the nonlinear optimization with the mesh adaptive direct algorithm solver and the dual decomposition method, respectively. The numerical results validate our analytical outcomes. For example, system delay decreases approximately 10 times if the traffic load of macro BS is decreased by 50%. In addition, we present a comparison of the impact of traffic reduction and consumed bandwidth due to offloading by means of LAPs on the cellular network, which confirms the efficiency of the proposed approach.