A new kind of even and odd nonlinear coherent states (EONLCS) is constructed. Using the numerical computation method, the non-classical properties such as squeezing, amplitude-squared squeezing, anti-bunching and phase probability distribution of the new EONLCS are investigated. The results show that, in the different ranges of the parameter |λ|, the new EONLCS exhibits amplitude-squared squeezing in the directions Y1 and Y2. The squeezing effect is shown in the direction X2 for new even nonlinear coherent states, and the anti-bunching effect is shown for new odd nonlinear coherent states. Moreover, we find that the new EONLCS exhibit different quntum interference properties by studying the probability distributions of the states.