A proper orthogonal decomposition (POD) method is applied to a usual second-order time accurate Crank-Nicolson finite element (CNFE) formulation for parabolic equations such that it is reduced into a second- order time accurate CNFE formulation with fewer degrees of freedom and high enough accuracy. The errors between the reduced second-order time accurate CNFE solutions and the usual second-order time accurate CNFE solutions are analyzed. It is shown by numerical examples that the reduced second-order time accurate CNFE formulation can greatly save degrees of freedom in a way that guarantees a sufficiently small errors between the reduced second-order time accurate CNFE solutions and the usual second-order time accurate CNFE solutions. The time step of the reduced second-order time accurate CNFE formulation is ten times that of the first-order time accurate reduced finite element formulation such that it could obtain very quickly the numerical solution at the moment wanted, alleviate the computer truncation error, and improve rate and accuracy in the computational process. Moreover, it is also shown that the reduced second-order time accurate CNFE formulation is feasible and efficient solving parabolic equations.