Abstarct: Quantum discord is a kind of correlation beyond the quantum entanglement. It is defined as the difference between mutual information and classical correlations. Quantum discord can be nonzero even for the cases without any entanglement. So separable density matrices are not sufficient reason for zero discord and zero entanglement does not imply absence of the quantum correlations. Considering the coins being used, asymptotic reduced density matrix of the quantum walks may be X-state or not. For example, quantum walk with the Bell-coin has reduced density matrix in the form of X-state, while for quantum walk with Grover and Hadamard is not, but doesn’t have more independent variable. In this work we consider different types of coins such as Bell, Grover and Hadamard and study all types of the quantum correlations for them. We also consider correlation between coin and the position as well as quantum discord between subsystems.