In this paper, our main purpose is to establish the existence of infinitely positive bounded entire solutions of second order quasilinear elliptic systems. These extend a work of Zuodong Yang [Zuodong Yang, Existence of positive bounded entire solutions of quasilinear elliptic equations, Appl. Math. Comput. 156 (2004) 743–754], which considered the single quasilinear elliptic equation. These extend also a work of Kawano and Kusano [N. Kawano, T. Kusano, On positive entire solutions of a class of second order semilinear elliptic systems, Math. Zeitschrift 186 (3) (1984) 287–297] which studied the semilinear elliptic equation.