Abstarct: In today's world, the need for high speed and data rate has led to the proposal of new generation wireless telecommunication networks. Several basic technologies have played a very important role in the development of new generation systems. One of these technologies is massive MIMO systems that were introduced in the 2010. In these systems, a large number of antennas are used in the baxse stations and spatial gain can be used through them. Detecting the signal accurately from the transmitter to the receiver is a key focus in these systems. Optimal detection in massive MIMO systems is an NP-hard problem, as a result, one of the fundamental challenges in this field is to have detectors with low complexity and performance close to the optimal detector. For this purpose, various detection methods have been proposed, but these methods have problems and their performance is far from the optimal detector. Thus, the necessity for a novel detector exhibiting performance closely resembling that of the optimal detector is essential. Therefore, in this thesis, an algorithm for detection with low complexity is proposed. In the proposed method, an iterative algorithm is used for the purpose of detection in massive MIMO systems, which has two stages. In the first step, an estimate of the transmitted signal is obtained using the modified GS method. In the second step, the detection error is corrected with the ADMM algorithm. Similar results show that the performance of the proposed detector is close to the performance of the optimal detector.