Network selection is one of the hot issues in the fusion of heterogeneous wireless networks (HWNs). However, most of previous works only consider selecting single-access network, which wastes other available network resources, rarely take account of multi-access. To make full utilization of available coexisted networks, this paper proposes a novel multi-access selection algorithm based on joint utility optimization for users with multi-mode terminals. At first, the algorithm adopts exponential smoothing method (ESM) to get smoothed values of received signal strength (RSS). Then we obtain network joint utility function under the constraints of bandwidth and number of networks, with the consideration of trade-off between network benefit and cost. At last, Lagrange multiplier and dual optimization methods are used to maximize joint utility. Users select multiple networks according to the optimal association matrix of user and network. The simulation results show that the proposed algorithm can optimize network joint utility, improve throughput, effectively reduce vertical handoff number, and ensure Quality of Service (QoS).