Summary: A new polynomial system of hypergeometric type is defined by means of the relativistic Laguerre polynomial system \(\big\{L_n^{(\alpha,N)}(x)\big\}_{n=0}^\infty\). These polynomials, denoted by \(\big\{y_n^{(N)}(x;a,b)\big\}_{n=0}^\infty\), are called relativistic generalized Bessel polynomials because they reduce, in the non-relativistic limit (\(N\to\infty\)), to the generalized Bessel polynomials first considered by Krall and Frink. Some main properties of the new set of orthogonal polynomials are derived.