Context. There is a considerable deficiency in the number of known supernova remnants (SNRs) in the Galaxy compared to that expected. This deficiency is thought to be caused by a lack of sensitive radio continuum data. Searches for extended low-surface brightness radio sources may find new Galactic SNRs, but confusion with the much larger population of H II regions makes identifying such features challenging. SNRs can, however, be separated from H II regions using their significantly lower mid-infrared (MIR) to radio continuum intensity ratios. Aims. Our goal is to find missing SNR candidates in the Galactic disk by locating extended radio continuum sources that lack MIR counterparts. Methods. We use the combination of high-resolution 1-2 GHz continuum data from The HI, OH, Recombination line survey of the Milky Way (THOR) and lower-resolution VLA 1.4 GHz Galactic Plane Survey (VGPS) continuum data, together with MIR data from the Spitzer GLIMPSE, Spitzer MIPSGAL, and WISE surveys to identify SNR candidates. To ensure that the candidates are not being confused with H II regions, we exclude radio continuum sources from the WISE Catalog of Galactic H II Regions, which contains all known and candidate H II regions in the Galaxy. Results. We locate 76 new Galactic SNR candidates in the THOR and VGPS combined survey area of 67.4 • > > 17.5 • , | b | ≤ 1.25 • and measure the radio flux density for 52 previously-known SNRs. The candidate SNRs have a similar spatial distribution to the known SNRs, although we note a large number of new candidates near 30 • , the tangent point of the Scutum spiral arm. The candidates are on average smaller in angle compared to the known regions, 6.4 ± 4.7 versus 11.0 ± 7.8 , and have lower integrated flux densities.Conclusions. The THOR survey shows that sensitive radio continuum data can discover a large number of SNR candidates, and that these candidates can be efficiently identified using the combination of radio and MIR data. If the 76 candidates are confirmed as true SNRs, for example using radio polarization measurements or by deriving radio spectral indices, this would more than double the number of known Galactic SNRs in the survey area. This large increase would still, however, leave a discrepancy between the known and expected SNR populations of about a factor of two.