We present a new class of non-abelian spin-singlet quantum Hall states, generalizing Halperin's abelian spin-singlet states and the Read-Rezayi non-abelian quantum Hall states for spin-polarized electrons. We label the states by (k,M) with M odd (even) for fermionic (bosonic) states, and find a filling fraction $\nu=2k/(2kM+3)$. The states with M=0 are bosonic spin-singlet states characterized by an SU(3)_k symmetry. We explain how an effective Landau-Ginzburg theory for the SU(3)_2 state can be constructed. In general, the quasi-particles over these new quantum Hall states carry spin, fractional charge and non-abelian quantum statistics.