Quantum spin Hall (QSH) insulators are two-dimensional electronic materials that have a bulk band gap like an ordinary insulator but have topologically protected pairs of edge modes of opposite chiralities. To date, experimental studies have found only integer QSH insulators with counter-propagating up-spins and down-spins at each edge leading to a quantized conductance G0=e^2/h. Here we report transport evidence of a fractional QSH insulator in 2.1-degree-twisted bilayer MoTe2, which supports spin-Sz conservation and flat spin-contrasting Chern bands. At filling factor v = 3 of the moiré valence bands, each edge contributes a conductance 3/2 G0 with zero anomalous Hall conductivity. The state is likely a time-reversal pair of the even-denominator 3/2-fractional Chern insulators. Further, at v = 2, 4 and 6, we observe a single, double and triple QSH insulator with each edge contributing a conductance G0, 2G0 and 3G0, 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.