For a powerful cryptographic system, high-quality random number streams are essential. Those raw pseudo-random number generators (PRNG) that are used to generate high-quality random numbers have some disadvantages, such as failure to meet the R4 security requirement. Therefore, use of random number sequences generated by these generators in a cryptographic system puts the entire system at risk. This study proposes a new hybrid PRNG by means of an additional input introduced to transition and output functions used in a raw PRNG system in order to eliminate this risk. The additional inputs to the designed system have been implemented via the true random number generator developed by using the Sprott 94 G chaotic system on FPGA. The random number streams obtained from the recommended hybrid structure have been subjected to the NIST 800.22 and FIPS statistical test, which have given good results. According to these results, it has been proved that the recommended hybrid PRNG system meets the R4 security requirement and can be used in cryptographic applications.