Under the condition of unbalance grid voltage, traditional phase-locked loop (PLL) is incapable to track the frequency and phase of the voltage, and fails to get the positive and negative sequence components of the grid voltage directly. To solve this problem, a PLL algorithm based on adaptive observer in the fixed reference coordinates is presented. The adaptive observer model and gain matrix for grid angular frequency estimation is designed. By means of Lyapunov function definition, the adaptive law for the grid angular frequency is deduced. The proposed PLL algorithm not only can observe the frequency and phase angle of the grid voltage, but also can get the positive and negative sequences signals. Simulation and experimental results prove that PLL based on the adaptive observer has advantage of high precision, fast dynamic response and so on. Its advantages are more prominent in the unbalance conditions, so it can provide a reliable control foundation for the improvement of wind energy converter.