The popular RSA cryptosystem, based on the problem of integer factorization can widely be seen in practice even today. Since its inception, several enhancements and generalizations of RSA are proposed including its several multi-prime variants where the RSA modulus is a product of more than two primes. In this paper, we propose a generalized multi-moduli RSA cryptosystem (GMMRSA) which is a multi-prime RSA but with more than one modulus. We show that this multi-moduli approach yields a more secure cryptosystem than a multi-prime RSA with a single modulus without compromising its computational and time efficiencies.