In this paper, various nonlinear dynamic behaviors of distributed feedback semiconductor laser (DFB-SL) subjected to self-delayed optical and electrical feedback are studied numerically. The results show that the DFB-SL output presents a variety of nonlinear dynamic states such as single-period, quasi-period, and multi-period under different optical feedback intensities. When the external light feedback reaches a certain intensity, the laser output enters a chaotic regime. When the optical feedback intensity is small, a variety of nonlinear dynamic states will appear in the DFB-SL output under different electrical feedback intensities. When the optical feedback intensity is large, the single-period dynamic state cannot be obtained by changing the electrical feedback intensity. The optical feedback and electrical feedback delay time also have a significant influence on the nonlinearity of DFB-SL. When their time delays match, the relaxation oscillation of the laser is enhanced and exhibits a single-period state. And time mismatch may lead to chaos or instability. The bias current also affects the dynamic state, however, the direction of evolution of the dynamic states is not unidirectional as the current changes unidirectionally. When the DFB-SL is in a single-period state, changing the bias current will result in the change of the single-cycle oscillation frequency. These findings provide an important theoretical basis for applying the self-delayed feedback DFB-SL to microwave photonic signal processing and secure optical communication, as well as experimental means for conducting various nonlinear scientific researches.