Within the framework of the effective mass and adiabatic approximation, the electron transport through an InAs/InP cylindrical quantum wire is studied by using the transfer matrix method. The coherent and escape tunneling processes are analyzed in detail. Influence of external voltage and structure size on the dwell time and escape time are discussed theoretically. A resonant phenomenon of the dwell time for different electron longitudinal energies is observed. A peak value of dwell time appearing at some positions of the bound state increases as the energy level decreases. When a bias is applied on this system along the growth direction, all the peaks of the dwell time shift towards the lower energy and become higher with increasing bias. Furthermore, it can be seen that the asymmetry of structure affects the dwell time obviously. Different results are obtained with the increase of asymmetry of the structure, which can be attributed to a competition between the transmission probabilities through the whole structure and that through a single barrier. Besides, the coherent and escape tunneling processes are also investigated by using a finite-difference method between two asymmetrically coupled quantum disks. It is found that the coherent electron remains oscillating in the two coupled disks. When the right barrier thickness of the nanowire is decreased, a roughly exponential decay of the oscillation charge trapped in both quantum disks is observed. The oscillating period is not affected by the right barrier thickness. However, a great influence of the middle barrier on the oscillation period can be found easily.