In this paper we consider the hyponormality of Toeplitz operators $T_{varphi}$ on the Bergman space $L^2_a(mathbb{D})$ with symbol in the case of function f + $overline{g}$ with polynomials f and g. We present some necessary conditions for the hyponormality of $T_{varphi}$, under certain assumptions about the coefficients of ${varphi}$.