A theoretical light curve for the 1999 outburst of U Scorpii is presented in order to obtain various physical parameters of the recurrent nova. Our U Sco model consists of a very massive white dwarf (WD) with an accretion disk and a lobe-filling, slightly evolved, main-sequence star (MS). The model includes a reflection effect by the companion and the accretion disk together with a shadowing effect on the companion by the accretion disk. The early visual light curve (with a linear phase of t ~ 1-15 days after maximum) is well reproduced by a thermonuclear runaway model on a very massive WD close to the Chandrasekhar limit (M_WD = 1.37 ± 0.01 M), in which optically thick winds blowing from the WD play a key role in determining the nova duration. The ensuing plateau phase (t ~ 15-30 days) is also reproduced by the combination of a slightly irradiated MS and a fully irradiated flaring-up disk with a radius ~1.4 times the Roche lobe size. The cooling phase (t ~ 30-40 days) is consistent with a low-hydrogen content of X ≈ 0.05 of the envelope for the 1.37 M WD. The best-fit parameters are the WD mass of M_WD ~ 1.37 M, the companion mass of M_MS ~ 1.5 M (0.8-2.0 M is acceptable), the inclination angle of the orbit (i ~ 80^°), and the flaring-up edge, the vertical height of which is ~0.30 times the accretion disk radius. The duration of the strong wind phase (t ~ 0-17 days) is very consistent with the BeppoSAX supersoft X-ray detection at t ~ 19-20 days because supersoft X-rays are self-absorbed by the massive wind. The envelope mass at the peak is estimated to be ~3 × 10^-6 M, which is indicates an average mass accretion rate of ~2.5 × 10^-7 M yr^-1 during the quiescent phase between 1987 and 1999. These quantities are exactly the same as those predicted in a new progenitor model of Type Ia supernovae.