The adaptive beamforming algorithm-minimum variance distortionless response (MVDR) has been studied based on the electronically steerable parasitic array radiator (ESPAR) antenna. The ESPAR antenna uses a single radio-frequency (RF) front end, and its beamforming is achieved by adjusting reactance loads of parasitic elements coupled to the central active element. In the proposed beamforming method, the MVDR beamformer optimizes weights applied to outputs of beams. The optimization problem is formulated as a second-order-cone programming (SOCP) problem including a Euclidean distance metric to approximate the optimal equivalent weight vector to a feasible solution. Then the ESPAR beampattern design strategy iterates between the SOCP problem and a simple projection of reactance loads. The simulations show that the proposed MVDR beamforming method based on an ESPAR antenna gives a beam steering at the desired direction and placing nulls at the interfering directions, and it converges fast. However, when the desired source is close to the interferer, the output signal-to-interference-plus-noise ratio (SINR) degrades and where we use the interference-plus-noise sample covariance matrix to improve the beamforming performance.