The absence of both the inversion symmetry and out-of-plane mirror symmetry together with spin-orbit coupling (SOC) can induce novel electronic and piezoelectric properties. In this work, the piezoelectric properties along with carrier mobilities of Janus monolayer XTeI (X=Sb and Bi) are studied by density functional theory (DFT)... By using generalized gradient approximation (GGA) plus SOC, they are found to be indirect gap semiconductors with the Rashba spin splitting. The piezoelectric tensors of Janus monolayer XTeI (X=Sb and Bi) are reported by using density functional perturbation theory (DFPT). Due to lacking both the inversion symmetry and out-of-plane mirror symmetry for Janus monolayer XTeI (X=Sb and Bi), both in-plane and out-of-plane piezoelectric effects can be observed, and the large piezoelectric coefficients are predicted (e.g. $d_{11}$=12.95 pm/V for SbTeI and $d_{11}$=8.20 pm/V for BiTeI), which are comparable and even higher than ones of many other two-dimensional (2D) materials and other well-known bulk piezoelectric materials, especially for out-of-plane piezoelectric coefficients. With GGA+SOC, the high electron carrier mobilities are obtained, and the electron mobility of BiTeI along armchair direction reaches up to about 1319 $\mathrm{cm^2V^{-1}s^{-1}}$. The carrier mobility shows a rather pronounced anisotropy between electron and hole/armchair and zigzag directions. It is found that tensile strain can improve the piezoelectric coefficients $d_{11}$ of Janus monolayer XTeI (X=Sb and Bi). For example, at 4\% strain, the $d_{11}$ of SbTeI (BiTeI) is up to 20.12 pm/V (11.48 pm/V), compared with unstrained 12.95 pm/V (8.20 pm/V). Our works imply Janus monolayer XTeI (X=Sb and Bi) have potential applications in flexible electronics and piezoelectric devices, and can stimulate further experimental works. (read more)