As the wireless technology evolves, one can access the Internet almost everywhere via many wireless access networks such as wireless LAN and GPRS. People would like to use the wireless networks with high data rate, large coverage and low cost. Some networks such as GPRS can provide large coverage, but they only provide low data rate; some networks like wireless LAN can provide high data rate, but the access points are not widely deployed. None of the wireless networks can meet all requirements of a mobile user. Heterogeneous networks solve parts of the problem. In heterogeneous networks, users can roam among different kind of networks such as 802.11 wireless LAN and GPRS through vertical handoffs. But in heterogeneous networks, each kind of wireless networks provide different quality of services. Users roaming among the wireless networks will suffer enormous change of quality of services. The paper proposed three access network selection strategies that keep mobile users staying in the wireless networks with higher quality services longer and thus improves the average available bandwidth and decreases the call blocking probability.