This paper presents decoupled second-order accurate algorithms based on Crank-Nicolson LeapFrog (CNLF) scheme for the evolution Boussinesq equations. The proposed algorithms deal with the spatial discretization by finite element method and treat the temporal discretization by CNLF method. For the nonlinear term in the Boussinesq equations, the semi-implicit method is used. Unconditional stability and error estimate of the numerical algorithm are proven. Some numerical tests are presented to justify the theoretical analysis.