An automatic vision-based sewer inspection plays a key role of sewage system in a modern city. Recent advances focus on utilizing deep learning model to realize the sewer inspection system, benefiting from the capability of data-driven feature representation. However, the inherent uncertainty of sewer defects is ignored, resulting in the missed detection of serious unknown sewer defect categories. In this paper, we propose a trustworthy multi-label sewer defect classification (TMSDC) method, which can quantify the uncertainty of sewer defect prediction via evidential deep learning. Meanwhile, a novel expert base rate assignment (EBRA) is proposed to introduce the expert knowledge for describing reliable evidences in practical situations. Experimental results demonstrate the effectiveness of TMSDC and the superior capability of uncertainty estimation is achieved on the latest public benchmark.