Our paper studies the optical solitons for the Kundu–Eckhaus (KE) equation with quintic nonlinearity and Raman effect. By applying the improved modified extended tanh-function method, many soliton solutions can be obtained such as bright soliton solutions, dark soliton solutions, and the singular soliton solution. In addition, we can obtain various types of solutions, namely, singular periodic solutions, exponential solutions, rational solutions, Jacobi elliptic solutions and Weierstrass elliptic doubly periodic solutions. Moreover, some selected solutions are illustrated graphically to show the physical nature and the characteristics of the obtained solutions.