Random Number Generators (RNGs) are applied in a wide variety of cryptographic operations such as cryptographic computer security protocols, encryption algorithms, and keystreams. Stream ciphers employ an encryption transformation which varies with time. These algorithms transform a short random key sequence into a long Pseudorandom Number Generator (PRNG) sequence, termed keystream, which, in turn, is deployed for the encryption or decryption of the message into ciphertext or plaintext message. This paper presents a PRNG which relies on Rabbit cipher to generate a 128-bit keystream, with feedback as the initial vector for PRNG. The proposed PRNG produces a sequence of bits that have a semi-random distribution. This new generator helps develop a range of cryptographic applications to enhance system security. Its performance is evaluated in terms of implementation aspects, security properties, and statistical test for randomness. The proposed PRNG proved to be efficient with regard to its speed and security.