The minimum variance distortionless response is known to be sensitive to covariance matrix error and steering vector mismatch. An extension of the conventional linear constraint minimum variance (LCMV) method is proposed where the desired response vector is complex numbers instead of real numbers. Through adding a phase constraint on the desired output response, this method maintains a distortionless magnitude response together with phase response. Numerical results demonstrate that the method usually gives good robustness against the covariance error and steering vector mismatch.