Spectrum sensing is an essential functionality that enables cognitive radios (CR) to detect spectral holes and to opportunistically use under-utilized frequency bands without causing severe interference to primary users (PU). The state of art for wideband spectrum sensing is given by Multiband Joint Detection (MJD). Constraints on utilization and interference have to be imposed to solve the optimization problem. Unfortunately，because of the nonlinearity of constraints, the optimization problem may not solved efficiently. In this paper, a method based on second-order cone programming (SOCP) is proposed to solve the optimization problem, in which highly nonlinear constraints are approximated through second order Taylor expansion, and successfully incorporated into a SOCP framework. Simulations are presented to illustrate the performance of the proposed method.