A magnetic property of the one dimensional spin-7/2 Blume-Capel model under the magnetic field has been investigated by means of transfer matrix method. Thermodynamic response functions are also obtained for varying values of reduced thermodynamic temperature and scaling magnetic field. We have seen that the crystal field strongly affects magnetic plateau mechanism. Our simulation results demonstrate that the plateau becomes smoother when the value of the temperature increased. Entropy of the system goes to zero rapidly for positive crystal field values so we see only saturation values of the system. We observed that the minimum of specific heat tends to shift to the relatively lower thermodynamic temperature regions as the strength of the crystal field is increased.