A fast explicit finite difference method (FEFDM), derived from the differential equations of one-dimensional steady pipe flow, was presented for calculation of wellhead injection pressure. Recalculation with a traditional numerical method of the same equations corroborates well the reliability and rate of FEFDM. Moreover, a flow rate estimate method was developed for the project whose injection rate has not been clearly determined. A wellhead pressure regime determined by this method was successfully applied to the trial injection operations in Shihezi formation of Shenhua CCS Project, which is a good practice verification of FEFDM. At last, this method was used to evaluate the effect of friction and acceleration terms on the flow equation on the wellhead pressure. The result shows that for deep wellbore, the friction term can be omitted when flow rate is low and in a wide range of velocity the acceleration term can always be deleted. It is also shown that with flow rate increasing, the friction term can no longer be neglected.