Supplemental lighting is required for the production of high-quality vegetable transplants in greenhouses when the photosynthetic daily light integral (DLI) is low. Light-emitting diodes (LEDs) are a promising alternative to high-pressure sodium (HPS) lamps. However, there are a limited number of studies that have evaluated how LED supplemental lighting spectral quality beyond blue (B) and red (R) radiation influences plant growth and development. Seeds of hybrid greenhouse seedless cucumber ‘Elsie’ (Cucumis sativus), tomato ‘Climstar’ (Solanum lycopersicum), and pepper ‘Kathia’ (Capsicum annuum) were sown and placed into a dark growth chamber until radicle emergence. Seedlings were grown in a greenhouse at a 25 °C constant temperature set point and under five lighting treatments. The supplemental lighting treatments delivered a total photon flux density (TPFD) of 120 μmol·m−2·s−1 for 16 h·d−1 based on an instantaneous threshold from HPS lamps or LEDs [three treatments composed of B (400–500 nm), R (600–700 nm), white, and/or far-red (FR; 700–800 nm) LEDs], and a control that delivered 25 μmol·m−2·s−1 from HPS lamps (HPS25). The LED treatments defined by their wavebands (TPFD in μmol·m−2·s–1) of B, green (G, 500–600 nm), R, and FR radiation were B20G10R75FR15, B25R95, and B30G30R60; whereas the HPS treatments emitted B7G57R47FR9 (HPS120) and B1G13R9FR2 (HPS25). Generally, cucumber, pepper, and tomato transplants under B30G30R60 and HPS120 supplemental lighting had the greatest stem diameter. Fresh weight and leaf area of all three species was greater when G radiation replaced R or B radiation. For example, leaf area and fresh weight of cucumber, tomato, and pepper increased (by 33%, 22%, and 49%; and 35%, 14%, and 56%, respectively) for plants under B30G30R60 supplemental lighting compared with plants under B25R95 supplemental lighting. The most compact cucumber and pepper transplants were those grown under B25R95 supplemental lighting, and the most compact tomatoes were those grown under the HPS25 (control) and B25R95 supplemental lighting. Tomato transplants under treatments providing ≥30 μmol·m−2·s−1 of G radiation had an increased incidence of leaf necrosis. From this study, we conclude that plant responses to supplemental lighting quality are generally genera-specific, and therefore high-wire transplants should be separated by genera to optimize production and quality. However, additional studies are required to provide complete LED supplemental lighting recommendations.