The stationary probability density function (PDF) solutions of the responses of stochastic dynamic oscillators with even nonlinearity under parametric excitation on velocity are analyzed with exponential-polynomial closure (EPC) method. As there is parametric excitation, adjustable weighting functions are introduced in the EPC procedure for convergent solution when the parametric excitation is strong. The effectiveness of EPC solution procedure is investigated through several oscillators with even nonlinearity subjected to both external excitation and parametric excitation on velocity. Numerical analysis shows that the statistical properties of system responses are much different from those of oscillators with only odd nonlinearity. Numerical results show that the PDFs obtained with the EPC procedure agree well with those from Monte Carlo simulation.