GNSS carrier phase integer ambiguity resolution is the key for higher precision positioning and navigation. Due to more ambiguities with the multiple frequencies per system, the successful resolution of all ambiguities may not always be possible. However, a subset of the ambiguities can still be possible. In addition, resolving all ambiguities will increase the computational burden, and has slow convergence. In order to solve the problem, partial ambiguity fixing is applied to estimate the ambiguity in this paper. This paper first introduces the principle of ambiguity resolution and the concept of success rate. Then based on this background, the selection principle of an optimal subset is proposed and the algorithms are given. Simulation results show that, partial ambiguities by means of the presented method in this paper can be possible but full ambiguities can not. And resolving a subset of ambiguities can not only improve the ambiguity resolution performance and reliability but also reduce the convergent-time.