Quantum spin Hall (QSH) insulators are two-dimensional electronic materials that have a bulk band gap similar to an ordinary insulator but have topologically protected pairs of edge modes of opposite chiralities. So far, experimental studies have found only integer QSH insulators with counter-propagating up-spins and down-spins at each edge leading to a quantized conductance G = e/h (with e and h denoting the electron charge and Planck's constant, respectively). Here we report transport evidence of a fractional QSH insulator in 2.1° twisted bilayer MoTe, which supports spin-S conservation and flat spin-contrasting Chern bands. At filling factor ν = 3 of the moiré valence bands, each edge contributes a conductance with zero anomalous Hall conductivity. The state is probably a time-reversal pair of the even-denominator 3/2-fractional Chern insulators. Furthermore, at ν = 2, 4 and 6, we observe a single, double and triple QSH insulator with each edge contributing a conductance G, 2G and 3G, respectively. Our results open up the possibility of realizing time-reversal symmetric non-abelian anyons and other unexpected topological phases in highly tunable moiré materials.