  We investigate the pure penguin decays $B\to \pi\phi$ in the Standard
Model(SM) and in the Constrained Minimal Supersymmetric Standard Model (CMSSM)
using the QCD factorization approach and consider the Sudakov effects in the
twist-3 contribution. We find ${\rm Br}(B^-\to \pi^-\phi) = (1.95-5.70)\times
10^{-9}$ in SM and $(1.1-2.4)\times 10^{-8}$ in CMSSM with large $\tan\beta $
which is about one order of magnitude larger than that in SM.
