This paper presents a direct measurement of the differential
B^+ and B^0 cross-sections, d sigma/dp_T, in ppbar collisions at sqrt s =
1.8 TeV using a sample of 74 pb^-1 accumulated by the Collider Detector
at Fermilab (CDF).  The cross-sections are measured in the central
pseudorapidity region |eta| < 1 for p_T(B) > 6.0 GeV/c by fully reconstructing
the B meson decays B^+ -> J/psi K^+ and B^0 -> J/psi K^*0(892), where
J/psi -> mu^+mu^- and K^*0 -> K^+ pi^-.  The integrated B meson cross-section
for p_T(B) > 6.0 GeV/c is determined to be sigma(B^-) = 2.54 +/- 0.22 +/- 0.53
mu b.