In this paper, we formulate an intermediate boson (denoted as IB) theory based on the following assumptions: there are 8 images ω1,…,ω8 of IB, transforming as the octet of SU3, coupling with 8-dimensional hadron current to form an unitary singlet Lagrangian Lw; but either in real or in virtual states, only 4 kinds of particles(W±, W0, W0-4 linear combinations of ω1,…,ω8) can occur. The incompletenessof virtual IB states, which is the very source of isospin and strangeness nonconservation in weak processes, can be described by a projection operator ξ=|W+>+| + |W->-|+|W0>0|+|W0>0| used for intermediate states. If assuming further the lepton currents to couple directly with W±, one can obtain a theory giving unified description for all weak processes. When applied to leptonic decays, our theory leads directly to that identical with Cabibbo's, and explains his hypothesis of "unit length" in a natural way (as a result of probability normalization). When applied to nonleptonic decays, our theory includes the |ΔI| = 1/2 rule.