Theoretical model of the singlet long-range Josephson transport is proposed. Taking into account the mismatch of the electron effective masses of majority and minority spin subbands the Eilenberger-like equations are obtained with renormalized effective exchange interaction. The critical Josephson current is calculated through ferromagnet nanowire. It is shown that the effective exchange field can be completely compensated and thereby the long-range spatial supercurrent arises. Within the proposed theoretical model, the long-range proximity effect observed in the Co single-crystalline nanowire (Wang et al., 2010) can be qualitatively understood.