  We present a lattice calculation of the B meson B-parameter B_B using the
NRQCD action. The heavy quark mass dependence is explicitly studied over a mass
range between m_b and 4m_b with the $O(1/m_Q)$ and $O(1/m_Q^2)$ actions. We
find that the ratios of lattice matrix elements $<O_N^{lat}>/<A_0^{lat}>^2$ and
$<O_S^{lat}>/<A_0^{lat}>^2$, which contribute to B_B through mixing, have
significant $1/m_Q$ dependence while that of the leading operator
$<O_L^{lat}>/<A_0^{lat}>^2$ has little $1/m_Q$ effect. The combined result for
B_B(m_b) has small but non-zero mass dependence, and the B_B(m_b) becomes
smaller by 10% with the 1/m_Q correction compared to the static result. Our
result in the quenched approximation at \beta=5.9 is B_{B_d}(5 GeV) =
0.75(3)(12), where the first error is statistical and the second is a
systematic uncertainty.
