The exponential form of even and odd pair coherent state (EOPCS) is constructed. The EOPCS is generalized to a finite dimensional EOPCS in the Hilbert space, and then its orthonormalized property, completeness relations and some noncalssical properties are discussed. It is shown that the finite dimensional EOPCS has normalized and completeness relations, but not orthogonal relations. By virtue of the numerical computation method, we find that, for any value of q, in different ranges of the parameter |ξ| the 5-dimensional EOPCS for the modes 1 and 2 exhibit anti-bunching effect and the photons between the two modes are always correlated. The different peak structures of the phase probability distributions for the 7-dimensional EOPCS show remarkably different quantum interference properties.