We have analyzed 18 quarters of long-cadence data of KIC 9145955 provided by Kepler, and extracted 61 oscillation frequencies from these high-precision photometric data. The oscillation frequencies include 7 l= 0 modes, 44 l = 1 modes, 7 l= 2 modes, and 3 l = 3 modes. We identify l = 0 modes asp modes and l= 2 modes as p-dominated modes. For l = 1 modes, all of them are identified as mixed modes. These mixed modes can be used to determine the size of the helium core. We conduct a series of asteroseismic models and the size of the helium core is determined to be M-He = 0.210 +/- 0.002 M-circle dot and R-He = 0.0307 +/- 0.0002 R-circle dot. Furthermore, we find that only the acoustic radius tau(0) can be precisely determined with the asteroseismic method independently. The value of tau(0) is determined to be 0.494 +/- 0.001 days. By combining asteroseismic results and spectroscopic observations, we obtain the best-fitting model. The physical parameters of this model are M = 1.24 M-circle dot, Z = 0.009, alpha = 2.0, T-eff = 5069 K, log g = 3.029, R = 5.636 R-circle dot, and L = 18.759 L-circle dot. In addition, we think that the observed frequency F39 (96.397 mu Hz) is more appropriate to be identified as a mixed mode of the most p-dominated.