Many recent studies have been reported that the novel coronavirus (SARS-CoV-2) can spread through an airborne transmission route. Although ventilation is generally adopted to control viral infection through airborne transmission, a high ventilation rate will increase the energy consumption of air conditioning. Under such condition, the portable HEPA-filter air purifier might be an effective supplementary measure. However, past discussions on its efficacy in reducing indoor infection risks are limited. Therefore, this study aims to conduct a systematic investigation on the applicability of air purifier using Computational Fluid Dynamics (CFD) simulation. Two scenarios both with an air change rate of 0.5 1/h were considered. In Scenario a, a general room with size being 4 m × 5 m × 2.5 m (13.1 ft × 16.4 ft × 8.2 ft) was adopted. Viral contaminants were set as homogeneous emission. In Scenario b, a 6-mat bedroom with size being 2.7 m × 3.6 m × 2.5 m (8.9 ft × 11.8 ft × 8.2 ft) was adopted. Viral contaminants were assumed to be generated from a lying infector at 27 quanta/h constantly. The purifier was operated at a flow rate of 90 m3/h (3178 ft3/h). The results showed that a general household HEPA-filter air purifier has high effectiveness in removing indoor viral contaminants and infection risks. In Scenario b, to reach an infection probability of 0.2, it took a susceptible person only about 10 min of exposure time without purifier, but up to 50 min with a purifier. A larger flow rate can contribute to higher purifying effectiveness and a more thorough air mixing indoor. Moreover, the purifying effectiveness, distribution of contaminant concentration and infection probability were found to be influenced by the relative positions of the purifier inlet and outlet, ventilation air supply and exhaust, virus generation source, and indoor obstacles.