GPS is vulnerable to jamming because of extremely low signal power. Many anti-jamming techniques are studied for complement this vulnerability. Anti-jamming techniques using array antenna are most effective technique and these techniques are required the DOA estimates. MUSIC algorithm and Root-MUSIC Algorithm are typical algorithms used in DOA estimation. Two algorithms have different characteristics, so the choice of an algorithm may depends on many factors such as the environment and the system requirements. The analysis and performance comparison of both algorithms is necessary to choose the best method to apply. This paper summarizes the theory of MUSIC and Root-MUSIC algorithms. And this paper extends both algorithm to estimate two-dimensional angles. The software simulator of both algorithms are implemented to evaluate the performance. Root-MUSIC algorithm has the computational advantage on ULA. MUSIC algorithm is applicable to any antenna array. MUSIC shows better estimation performance when number of array element is small while the computational load of MUSIC is much higher than Root-MUSIC.