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We analyze the asymptotic symmetry of higher spin gravity with M × M matrix valued fields, which is given by rectangular W-algebras with su(M) symmetry. The matrix valued extension is expected to be useful for the relation between higher spin gravity and string theory. With the truncation of spin as s=2,3,... , n, we evaluate the central charge c of the algebra and the level k of the affine currents with finite c,k. For the simplest case with n=2, we obtain the operator product expansions amongdoi:10.1007/jhep02(2019)147 fatcat:okflzpauaje4fkryl5a55rtesy