In this paper, the authors define the notion of harmonic-arithmetic extended $(s_1,m_1)$- $(s_2,m_2)$ coordinated convex functions, establish a new integral identity, present some new Hermite–Hadamard type integral inequalities for harmonic-arithmetic extended $(s_1,m_1)$- $(s_2,m_2)$ coordinated convex functions, and derive some known results.