Two-dimensional phase unwrapping is the key step of the later data processing in the existing advanced metrology technologies such as optical interferometry, optical three-dimensional sensing measurement, satellite radar interferometry (SAR), and magnetic resonance imaging (MRI). In this paper, the anti-noise performance of three common spatial phase unwrapping algorithms, branch-cut phase unwrapping algorithm, minimum discontinuity algorithm, and fast phase unwrapping algorithm, are compared by simulating the situation of noise interference. The result shows that the minimum discontinuity algorithm has the best performance in anti-noise, but its time consuming is far greater than the other two algorithms. Two hybrid algorithms, combining the minimum discontinuity algorithm with the branch-cut phase unwrapping algorithm and the fast phase unwrapping algorithm respectively, are proposed considering the advantages and disadvantages of the three algorithms mentioned above. In these two proposed algorithms, the advantages of fast speed of branch-cut phase unwrapping algorithm and fast phase unwrapping algorithm are fully taken into account, and the advantage of the strong anti-noise of the minimum discontinuity algorithm is also exploited. These two combined algorithms guarantee both the speed and accuracy of the phase unwrapping. The effectiveness of two combined algorithms is verified by the results of simulation and actual experiment.