We study the rate and phi momentum distribution in semi-inclusive decays B-->phiX(s) induced by the quark level processes b-->phis and b-->phisg, in which the gluon is radiated from the internal charm quark loop or emitted from the virtual gluon of the strong penguin (inner bremsstrahlung) process. We find B(b-->phis)=6.7x10(-5) and B(b-->phisg)=3.8x10(-5). The momentum spectrum of phi produced by b-->phisg is very broad. With the cut \k(phi)\greater than or equal to2.0 GeV, B(b-->phis)=6.1x10(-5) (where the Fermi motion of the b quark in the B meson is described by a Gaussian), and B(b-->phisg)=1.0x10(-5). Because of the special nature of phi, many difficulties that hindered a reliable theoretical prediction for B-->eta'X-s decay are absent in the process B-->phiX(s). Therefore, theoretical predictions for B-->phiX(s) are relatively clean. Moreover, the clear experimental signature of the phi is of great help. Data for B-->phiX(s), both the branching ratio and the phi momentum distribution, would teach us about the strength of strong penguin processes which might be of great importance in the search for CP violation and for new physics at B factories.