This paper presents the results of a linear cryptanalysis of quasigroup block cipher. The quasigroup block cipher is being developed for resource constrained environments, especially SCADA systems. Here we determine if any key material can be found by conducting a linear cryptanalysis on a simplified quasigroup block cipher. Using Matsu''s algorithm we seek to determine a suitable linear approximation of the quasigroup block cipher, the number of plaintext-ciphertext pairs to test, and the amount of time and space required to mount a known-plaintext attack on the quasi-group block cipher. Since the quasigroup does not use a Feistel network, the focus of the linear cryptanalysis is on the keyed transformation during table lookup operations of the quasigroup in order to 1) determine how the key bits used during encryption impact the ciphertext and from this 2) find a linear approximation that is non-negligible. Our results showed that no key material is recovered using linear cryptanalysis and consequently quasigroup cipher is resistant to such an attack.