This paper presents a Laguerre polynomials-based parametrised model order reduction method for the parametric system in time domain. The method allows that the parametric dependence in system matrices is nonaffine. The method is presented via reducing an approximate polynomial parametric system based on Taylor expansion and Laguerre polynomials, resulting in a parametric reduced system that can accurately approximate the time response of the original parametric system over a wide range of parameter. The reduced parametric system obtained by proposed method can be implemented by two algorithms. Algorithm 1 is a direct way that is suitable for single-input multi-output parametric systems. Algorithm 2 is presented based on a connection to the Krylov subspace, which is efficient and suitable for multi-input multi-output parametric systems. The effectiveness of the proposed method is illustrated with two benchmarks in practical applications.