We confirm a massive sub-Neptune-sized planet on a P = 22.8 days orbit around the star TOI-1824 (Teff = 5200 K, V = 9.7 mag). TESS first identified TOI-1824 b (formerly TOI-1824.01) as an object of interest in 2020 April after two transits in Sector 22 were matched with a single transit in Sector 21. TOI-1824 was subsequently targeted for ground-based Doppler monitoring with Keck-HIRES and APF-Levy. Using a joint model of the TESS photometry, radial velocities, and Ca ii H and K emission measurements as an activity indicator, we find that TOI-1824 b is an unusually dense sub-Neptune. The planet has a radius Rp = 2.63 ± 0.15 R⊕ and mass Mp = 18.5 ± 3.2 M⊕, implying a bulk density of 5.6 ± 1.4 g cm−3. TOI-1824 b's mass and radius situate it near a small group of "superdense sub-Neptunes" (Rp ≲ 3 R⊕ and Mp ≳ 20 M⊕). While the formation mechanism of superdense sub-Neptunes is a mystery, one possible explanation is the constructive collision of primordial icy cores; such giant impacts would drive atmospheric escape and could help explain these planets' apparent lack of massive envelopes. We discuss TOI-1824 b in the context of these overdense planets, whose unique location in the exoplanet mass–radius plane make them a potentially valuable tracer of planet formation.