  First results of lattice QCD simulation on the nucleon tensor-charge $\delta
q$ are presented. From the quenched QCD simulations with the Wilson quark
action at $\beta = 5.7$ on a 16$^3\times$ 20 lattice and on a $12^3\times 20$
lattice, we find (i) the connected part $\delta q_{con.}$ is determined with
small statistical error, (ii) the disconnected part $\delta q_{dis.}$, which
violates the OZI rule, is consistent with zero, and (iii) the flavor-singlet
tensor charge $ \delta \Sigma (\mu^2 = 2 {\rm GeV}^2) = \delta u + \delta d +
\delta s$ takes 0.562(88) at $\beta=5.7$, which is in contrast with the
flavor-singlet axial charge $\Delta \Sigma = 0.1-0.3$.
