High-level ab initio calculations on the ground and the excited states of the SrH molecule have been carried out utilizing the multi-reference configuration interaction method plus Davidson correction (MRCI+Q) method, with small-core relativistic effective core potentials together with the corresponding correlation consistent polarized valence basis sets. The potential energy curves (PECs) of the 16 Lambda-S states have been obtained with the aid of the avoided crossing rule between electronic states of the same symmetry. The spectroscopic constants of the bound states were calculated, most of which have been reported for the first time, with those pertaining to the X-2 Sigma(+), A(2)Pi, B-2 Sigma(+), and A'(2)Delta states being in line with the available experimental and theoretical values. The calculated spin orbit matrix element indicates a strong interaction between the X-2 Sigma(+) and A(2 Pi) states in the Franck-Condon region. The spin-orbit coupling (SOC) splits the lowest strongly bound X-2 Sigma(+), A(2)Pi, A'(2)Delta, B-2 Sigma(+), and D-2 Sigma(+) states into 9 Omega states. For the D-2 Sigma(+) state, the SOC shifts the potential-well minimum to higher energy and shortens the bond length. The transition properties of the bound A-S states were predicated, including the transition dipole moments (TDMs), the Franck-Condon factors, and the radiative lifetimes. The lifetimes were calculated to be 34.2 ns (v'=0) and 55.0 ns (v'=0) for A(2)Pi and B-2 Sigma(+), in good agreement with the experimental results of 33.8 +/- 1.9 ns and 48.4 +/- 2.0 ns. (C) 2015 Elsevier Ltd. All rights reserved.