Approximate Message Passing (AMP) based optimal hybrid precoder/combiner for Millimetre-wave massive multiple-input multiple output (MIMO) system is presented. The optimal Hybrid precoder/combiner technique provides an antenna gain and high spectral efficiency. The increased sparsity in mmWave architecture, the computational complication of the Orthogonal Matching Pursuit scheme (OMP) scheme is increased and also avoids high estimation accuracy. To overcome shortcomings of the OMP scheme, Simultaneously OMP (SOMP), and least square scheme, AMP algorithm is developed. AMP scheme is used when used increased sparsity signal. AMP scheme is attain low computational complexity and high spectral efficiency when compared to the existing scheme.