Acousto-optic interaction can be used for ultrafast optical field control in passively mode-locked fiber lasers. Here, we propose the use of an intracavity acousto-optic mode converter (AOMC) with combination of a few-mode fiber Bragg gratings (FM-FBG) to achieve narrow linewidth mode-locked pulse output with switchable transverse mode and wavelength in a ring fiber laser. Due to the selectivity of the FM-FBG to the input mode, the output mode and wavelength can be adjusted in the mode-locked fiber laser based on a semiconductor saturable absorption mirror. In experiments, by adjusting the acoustic frequency imposed in the AOMC, the wavelength of mode-locked pulses was switched from 1551.52 nm to 1550.21 nm, retaining the repetition rate of 12.68 MHz. At the same time, the mode conversion from the ${\mathrm{LP}}_{01}$ to the ${\mathrm{LP}}_{11}$ mode in the FM-FBG transmission port was achieved. This laser may find application in mode-division multiplexing systems.