LTE system needs a powerful method for error control on the transmission channel. The error control method is based on adding parity bits to the signal data stream. These parity bits are used to detect the error in bits and also to correct them. Meanwhile, Convolution Encoding with Viterbi Decoding is a powerful method for Forward Error correction and Detection. In this paper, Matlab simulation Model as well as hardware architecture of LTE Viterbi decoder was designed with specifications according to 3GPP standard, where the code rate 1/3.