Abstract We report on the X-ray spectral analysis and time evolution of GRS 1739−278 during its 2014 outburst, based on MAXI/GSC and Swift/XRT observations. Over the course of the outburst, a transition from the low/hard state to the high/soft state and then back to the low/hard state was seen. During the high/soft state, the innermost disk temperature mildly decreased, while the innermost radius estimated with the multi-color disk model remained constant at ∼18 (D/8.5 kpc)(cos i/cos 30°)−1/2 km, where D is the source distance and i is the inclination of observation. This small innermost radius of the accretion disk suggests that the central object is more likely to be a Kerr black hole rather than a Schwardzschild black hole. Applying a relativistic disk emission model to the high/soft state spectra, a mass upper limit of 18.3 M⊙ was obtained based on the inclination limit i < 60° for an assumed distance of 8.5 kpc. Using the empirical relation of the transition luminosity to the Eddington limit, the mass is constrained to 4.0–18.3 M⊙ for the same distance. The mass can be further constrained to be no larger than 9.5 M⊙ by adopting the constraints based on the fits to the NuSTAR spectra with relativistically blurred disk reflection models (Miller et al. 2015, ApJ, 799, L6).