For point-like target, a wavefront sensorless adaptive optics correction method using deformable mirror (DM) eigen- modes is proposed and studied by simulation and experiment. A set of DM eigen- modes whose derivatives are orthogonal with each other is derived from the influence function matrix of DM to replace traditional Lukosz modes. The metric function is set as the mean square radius of far-field spot. The required correction amount of each mode is directly solved from the relationship between coefficients of DM eigen-modes and the metric function value. In the simulation,the correction accuracy using the two modes mentioned above is compared and the effect of modal bias coefficient variation on correction accuracy is analyzed. Closed-loop correction results for different aberration level are also given. The experimental system is set up based on a 37- channel DM. Experimental results show that low- order aberrations can be effectively corrected by the algorithm and the correction accuracy of DM eigen-modes is better than Lukosz modes.