Effect of higher nonlinearity to optical solitons in the medium of electromagnetically induced transparency is investigated theoretically. By applying semi-classical theory, the response of the medium to the optical field is obtained. Based on the feature of the medium and by using the wave theory, a cubic- quantic nonlinear Schrodinger equation describing the evolution of the optical wave is obtained. The linear and nonlinear susceptibilities of the medium determine the group velocity dispersion parameter, third- order and fifth- order nonlinearities of the nonlinear equation. It is found that the bright soliton and dark soliton can be induced under the presence of higher nonlinearity, and the occurrence of both solitons determined by the signs of the group velocity dispersion and third-order nonlinearity. When the former is negative while the latter is positive, bright soliton occurs; when both of them are negative, dark soliton occurs. The sign of the two parameters can be got by management of the frequency shift between the carrier frequency and the relative atomic transition. Compared with the general nonlinear Schrodinger equation, the cubic- quantic nonlinear Schrodinger equation has tough requirement of input and parameters condition for the occurrence of bright and dark solitons.