We have estimated the arrival time of interplanetary coronal mass ejection (ICME) shocks during solar cycle 23 (the period from 1996 to 2007) using the artificial neural network. Under our model, we could match 97% of the listed coronal mass ejection CME-ICME events selected by Cane and Richardson (2010) using the initial velocities of the ICME events. Whereas, when we used the ICME velocity at a distance 20R⊙, our model succeeded to match only 84% of the listed ICME events. The prediction of CME travel-time correlated to the initial speed of CMEs, we found a high correlation coefficient between initial speed of CME and calculated travel time under our model (R≈74) with power fitting. The prediction of ICME arrival time can be better estimated from initial speed and linear speed of CMEs more than from final speed or speed at 20 R⊙.