The Roy-type even and odd nonlinear coherent states in a finite-dimensional Hilbert space are constructed. Their amplitude-squared squeezing effect, orthonormalized property, unitary property and completeness relations are discussed. The results reveal the existence of unitary property, completeness relations and non-orthonormalized property. There exists the amplitude-squared squeezing effect for the Roy-type even and odd nonlinear coherent states when the phase θ of parameter β meets the fixed condition. The relations between conditions of squeezing effect and parameters s,r and function f(n) are given. Finally using the numerical method, it is found that in some different ranges of r, the amplitude-squared squeezing effect exists in Roy-type even and odd nonlinear coherent states field in a finite-dimensional Hilbert space when the parameters s,θ and Lamb-Dike parameter η are given as the fixed value.