In the paper [2], R. André-Jeannin studied a class of polynomials $U_{n}(p,q;x)$. In this paper we consider a new class of polynomials $U_{n,m}(p,q;x)$ and determine the coefficients $c_{n,k}(p,q)$ of these introduced polynomials. Also, we define the polynomials $f_{n,m}(p,q;x)$, which are the rising diagonal polynomials of $U_{n,m}(p,q;x)$.