Using underwater gliders to measure underwater acoustic signals is a new measurement method emerging with the development of platform technology. Although underwater gliders are relatively quiet due to the absence of propellers, vehicle noise generated during motion is still inevitable, which will affect the recorded acoustic data. In this paper, we analyze the self-noise characteristics of underwater gliders based on simulated data by CFD technology for the hydrodynamic flow noise and experimental data acquired in an anechoic-water-tank experiment for the mechanical noise. The mechanical noise covers noises generated by buoyancy regulating (increasing and reducing), pitch regulating, rudder regulating and CTD pump working. According to the analysis results, the flow noise and CTD pump working noise could be ignored for the experimental data processing of sea trials. An experiment was conducted with an acoustic Sea-Wing underwater glider in the South China Sea from July 31 to September 4, 2018. Two kinds of noisy data were recorded, including target signals and ambient noise. All the target signals could be recognized after convolution filtering, except during the buoyancy regulating periods due to the high noise spectrum level. For the recorded ambient noise, in addition to the buoyancy regulating noise, the rudder and pitch regulating noises affected the recorded data. Then based on the acquired knowledge, a joint convolution filtering and thresholding method is proposed to remove the rudder and pitch noises from recorded noisy data. Kernels extracted from data acquired in the anechoic-water-tank experiment are used in the convolution filtering to localize each regulating action and energy thresholding is adopted to determine the duration of each regulation. All the rudder and pitch noises are removed from the recorded noisy data.