Constructions of quantum field theory (QFT) has been getting attention from a lot of mathematicians and physicists. Especially, the proof of existence of $\phi_2^4$ and $\phi_3^4$ quantum field theory along with the analysis of the models is one of the significant results of the constructive QFT. In our work, we use the lace expansion introduced by Brydges, Helmuth and Holmes (CPAM,2021) as a tool to prove the existence of $\phi_2^4$ and $\phi_3^4$ quantum field theory. In this talk, we will introduce the lace expansion and show some estimates in our proof. This talk is based on joint work with Yucheng Liu (UBC), Akira Sakai (Hokkaido Uni) and Gordon Slade (UBC) which is still ongoing.