This paper addresses the problem of loop gain margins of multivariable feedback system. A frequency domain approach is proposed to accurately computing loop gain margins for multivariable feedback systems. With the help of vector mapping method, the loop gain margins problem is converted to some constrained optimization, which is solved numerically by the Lagrange multiplier and Newton-Raphson iteration algorithm. The proposed approach can determine all the stabilizing boundaries and provide exact gain margins in comparison with conservativeness of the linear matrix inequalities (LMI) results reported before. Crown Copyright (C) 2010 Published by Elsevier Ltd. All rights reserved.