In order to make the fiber laser operate in two different states simultaneously, the erbium-doped fiber laser with both nonlinear polarization rotation (NPR) technique and carbon nanotube saturable absorber (CNT-SA) was fabricated in this experiment. The intra-cavity birefringence-induced comb filter based on NPR effect was employed to realize the dual-wavelength operation, and the Q-switched and Q-switched mode-locking pulses could be achieved by utilizing the NPR technique and the CNT-SA together. Therefore, the coexistence of Q-switched and Q-switched mode-locking pulses could be obtained in the fiber laser by finely adjusting the cavity parameters. After filtering each wavelength, it was found that the lasing line at 1531.23 nm corresponded to the Q-switched pulse with repetition rate of 45.62 kHz, while the lasing line at 1557.18 nm corresponded to the Q-switched mode locking pulse. The Q-switched envelope repetition rate and pulse repetition rate of the Q-switched mode locking pulses are 45.62 kHz and 18.18 MHz, respectively. The experimental results would enhance the operation flexibility of fiber laser, and further expand its application in related fields.