An 888 nm pumped quasi-single-crystal-fiber (quasi-SCF) acousto-optic Q-switched Nd:YVO4 laser is experimentally demonstrated for the first time, where two closely jointed crystals with different side surface styles serve as a long thin medium to improve the pump absorption and alleviate thermal load. In continuous-wave operation, the highest output power can reach 38.7 W with corresponding optical-optical efficiency of 0.492. In Q-switched operation, the optical-optical efficiency increases from 0.347 to 0.476 and pulse duration varies from 15 ns to 32.8 ns when pulse repetition frequency increases from 30 kHz to 100 kHz. The measured beam quality factors M2 are 1.018 and 1.030, respectively. The quasi-SCF scheme enjoys the advantage of sufficient pump absorption and reduced amplified spontaneous emission, which is promising for further applications in high-power lasers.