Longitudimal and transverse normal zone propagations in the superconducting coil are analyzed and propagation velocity is derived from the heat balance equations in the propagating boundary region. The results of applying to the specific superconducting wire show that propagation velocity is linearly proportional to the transport current and increasing ramp current speeds up the longitudinal velocity by 1.22[m/s] under the applied field of 2T. Transient heat transfer has a significant effect on the normal zone propagation velocity and it decreases longitudinal velocity by 5.2[m/s] under the applied field of 2T as being compared to the steady-state heat transfer. Increasing ramp current speeds up the Z-axis transverse propagation velocity by 0.042[m/s] and transverse velocity of R and Z axis is costant regardless of the current flows.