  We present a lattice QCD calculation of the heavy quark expansion parameters
$\mu_{\pi}^2$ and $\mu_G^2$ for heavy-light mesons and heavy-light-light
baryons. The calculation is carried out on a 20$^3\times$48 lattice at $\beta$
= 6.0 in the quenched approximation, using the lattice NRQCD action for heavy
quarks. We obtain the parameters $\mu_{\pi}^2$ and $\mu_G^2$ in two different
methods: a direct calculation of the matrix elements and an indirect
calculation through the mass spectrum, and confirm that the both methods give
consistent results. We also discuss an application to the lifetime ratios.
