The quantum quench dynamics of the one-dimensional Ising model in transverse field is investigated using the quantum renormalisation group method. The analytic expression of concurrence $C(t)$ is obtained, where the initial state is a superposition state which is constructed from the eigenstates of pure Ising system. The effect of parameter $a$ in the period and range of concurrence are exhibited respectively in the vicinity of the critical point, which show scaling behaviour. When effective magnetic field $g$ is big enough, the maximum limit value is 1.0. However, the minimum value is different, which is also dependent on the evolved time $t$.