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A phase-only direct data domain least square (D3LS) algorithm based on the nonlinear conjugate gradient (CG) method is presented. The cost function is obtained via the normal D3LS algorithm as a first step, and then optimized with the nonlinear CG method to determine the optimum weight vector finally. As a phase-only adaptive algorithm, the proposed algorithm has a better simplicity on hardware implementation than conventional algorithms. Moreover, it processes only a single data snapshot with no use for the formation of the sample covariance matrix and matrix inversion operation. Therefore, it may be so effective in real-time processing. Simulation results show the proposed algorithm has a good signal recovery and interferences nulling performance.