  By performing large-scale density-matrix renormalization group simulations,
we investigate a one-dimensional correlated bosonic lattice model with a
synthetic spin-orbit coupling realized in recent experiments. In the insulating
regime, this model exhibits a symmetry-protected topological phase. This
symmetry-protected topological phase is stabilized by time-reversal symmetry
and it is identified as a Haldane phase. We confirm our conclusions further by
analyzing the entanglement spectrum. In addition, we find four conventional
phases: a Mott insulating phase with no long range order, a ferromagnetic
superfluid phase, a ferromagnetic insulating phase and a density-wave phase.
