In astronomical spectral analysis, class recognition is essential and fundamental for subsequent scientific research. The experts often perform the visual inspection after automatic classification to deal with low-quality spectra to improve accuracy. However, given the enormous spectral volume and inadequacy of the current inspection practice, such inspection is tedious and time-consuming. This article presents a visual analytics system named SpectrumVA to promote the efficiency of visual inspection while guaranteeing accuracy. We abstract inspection as a visual parameter space analysis process, using redshifts and spectral lines as parameters. Different navigation strategies are employed in the "selection-inspection-promotion" workflow. At the selection stage, we help the experts identify a spectrum of interest through spectral representations and auxiliary information. Several possible redshifts and corresponding important spectral lines are also recommended through a global-to-local strategy to provide an appropriate entry point for the inspection. The inspection stage adopts a variety of instant visual feedback to help the experts adjust the redshift and select spectral lines in an informed trial-and-error manner. Similar spectra to the inspected one rather than different ones are visualized at the promotion stage, making the inspection process more fluent. We demonstrate the effectiveness of SpectrumVA through a quantitative algorithmic assessment, a case study, interviews with domain experts, and a user study.