Abstract Extended very-high-energy (VHE; 0.1–100 TeV) γ-ray emission has been observed around several middle-aged pulsars and referred to as “TeV halos.” Their formation mechanism remains under debate. It is also unknown whether they are ubiquitous or related to a certain subgroup of pulsars. With 2321 days of observation, the High Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory detected VHE γ-ray emission at the location of the radio-quiet pulsar PSR J0359+5414 with >6σ significance. By performing likelihood tests with different spectral and spatial models and comparing the TeV spectrum with multiwavelength observations of nearby sources, we show that this excess is consistent with a TeV halo associated with PSR J0359+5414, though future observation of HAWC and multiwavelength follow-ups are needed to confirm this nature. This new halo candidate is located in a noncrowded region in the outer galaxy. It shares similar properties to the other halos but its pulsar is younger and radio-quiet. Our observation implies that TeV halos could commonly exist around pulsars and their formation does not depend on the configuration of the pulsar magnetosphere.