To circumvent the prohibitive complexity of linear minimum mean square error detection in a massive multiple-input multiple-output sys- tem, several iterative methods have been proposed. However, they can still be too complex and/or lead to non-negligible performance degra- dation. In this letter, a Chebyshev acceleration technique is proposed to overcome the limitations of iterative methods, accelerating the conver- gence rates and enhancing the performance. The Chebyshev accelera- tion method employs a new vector combination, which combines the spectral radius of the iteration matrix with the receiver signal, and also the optimal parameters of Chebyshev acceleration have also been de- fined. A detector based on iterative algorithms requires pre-processing and initialisation, which enhance the convergence, performance, and complexity. To influence the initialisation, the stair matrix has been pro- posed as the first start of iterative methods. The performance results show that the proposed technique outperforms state-of-the-art meth- ods in terms of error rate performance, while significantly reducing the computational complexity.