P₂-Packing is a typical NP-hard problem. This paper provides a further study on the structures of the P₂-packing problem, and proposes a kernelization algorithm that can obtain a kernel of size at most 7k, which greatly reduces the current best kernel 15k. Based on the kernelization algorithm, an improved parameterized algorithm with running time O^*(2^4.142k) is also presented, which greatly improves the current best result O^*(2^5.301k).