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We study Penner type matrix models in relation with the Nekrasov partitionfunction of four dimensional \mathcal{N}=2, SU(2) supersymmetric gauge theorieswith N_F=2,3 and 4. By evaluating the resolvent using the loop equation forgeneral \beta, we explicitly construct the first half-genus correction to thefree energy and demonstrate the result coincides with the correspondingNekrasov partition function with general \Omega-background, including higherinstanton contributions after modifying the relation of the Coulomb branchparameter with the filling fraction. Our approach complements the proof usingthe Selberg integrals directly which is useful to find the contribution in theseries of instanton numbers for a given deformation parameter.

\beta-deformed matrix model and Nekrasov partition function