Coded caching, which could significantly reduce the maximum amount of transmission rate during the peak traffic times in wireless network, has been widely studied recently. Apart from the transmission rate, sub-packetization $F$ reflecting the implementation complexity, is also concerned in coded caching. The grouping method proposed by Shanmugam et al. is well-known and widely used to reduce the sub-packetization level of the coded caching problem. In this paper, we propose a concatenating construction method for coded caching schemes, which generalizes the grouping method. Moreover, we demonstrate the advantage of our method in reducing the transmission rate over the grouping method. In particular, some new explicit schemes are obtained from previously known schemes. From one of these schemes, we can derive all the results by Tang and Ramamoorthy as special cases. Furthermore, the analysis and comparison of these new schemes are also performed.