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Let $G$ be a graph. We use $P_t$ and $C_t$ to denote a path and a cycle on$t$ vertices, respectively. A {\em diamond} is a graph obtained from twotriangles that share exactly one edge. A {\em kite} is a graph consists of adiamond and another vertex adjacent to a vertex of degree 2 of the diamond. A{\em gem} is a graph that consists of a $P_4$ plus a vertex adjacent to allvertices of the $P_4$. In this paper, we prove some structural properties to$(P_7, C_4,$ diamond)-free graphs, $(P_7, C_4,$ kite)-free graphs and $(P_7,C_4,$ gem)-free graphs. As their corollaries, we show that (\romannumeral 1)$\chi (G)\leq \max\{3,\omega(G)\}$ if $G$ is $(P_7, C_4,$ diamond)-free,(\romannumeral 2) $\chi(G)\leq \omega(G)+1$ if $G$ is $(P_7, C_4,$ kite)-freeand (\romannumeral 3) $\chi(G)\leq 2\omega(G)-1$ if $G$ is $(P_7, C_4,$gem)-free. These conclusions generalize some results of Choudum {\em et al} andLan {\em et al}.

Structure and coloring of some ($P_7,C_4$)-free graphs