In this paper, the pulsation behavior of high-amplitude delta Scuti star GSC 4552-1498 was analyzed. Using the high-precision photometric data from the Transiting Exoplanet Survey Satellite, two new independent frequencies F1 = 22.6424(1) day(-1 )and F2 = 28.6803(5) day(-1) were identified for this source, along with the fundamental one F = 17.9176(7) day(-1), which was previously known. In addition, the classical O - C analysis was conducted to give a new ephemeris formula of BJD(max) = T-0 + P x E= 2453321.534716(4) + 0.055811(0) x E. The O - C diagram reveals a continuous period increase, but the rate of (1/P)(dP / dt)= 1.11(3) x 10(-7) yr(-1) seems much larger (about hundreds) than predicted by evolution theories, which is long been noticed but not well understood, possibly related to nonlinear mode interaction. Based on frequency parameters (i.e., F, F1, and F2), a series of theoretical models were conducted by employing the stellar evolution code. It turns out that F1 should be a nonradial mode and F2 is the second overtone radial mode. Due to the mass-metallicity degeneracy, the stellar parameter of the star can however not be determined conclusively. We suggest high-resolution spectral observation is highly desired in the future to further constrain models. We note GSC 4552-1498 is located on the main sequence in the H-R diagram.