We study the effect on leptogenesis due to B - L cosmic strings of a U (1)B - L extension of the Standard Model. The disappearance of closed loops of B - L cosmic strings can produce heavy right handed neutrinos, NR's, whose CP-asymmetric decay in out-of-thermal equilibrium condition can give rise to a net lepton (L) asymmetry which is then converted, due to sphaleron transitions, to a baryon (B) asymmetry. This is studied by using the relevant Boltzmann equations and including the effects of both thermal and string generated non-thermal NR's. We explore the parameter region spanned by the effective light neutrino mass parameter over(m, ̃)1, the mass M1 of the lightest of the heavy right-handed neutrinos (or equivalently the Yukawa coupling h1) and the scale of B - L symmetry breaking, ηB - L, and show that there exist ranges of values of these parameters, in particular with ηB - L > 1011 GeV and h1 ≳ 0.01, for which the cosmic string generated non-thermal NR's can give the dominant contribution to, and indeed produce, the observed baryon asymmetry of the universe when the purely thermal leptogenesis mechanism is not sufficient. We also discuss how, depending on the values of ηB - L, over(m, ̃)1 and h1, our results lead to upper bounds on sin δ, where δ is the CP-violating phase that determines the CP asymmetry in the decay of the heavy right handed neutrino responsible for generating the L-asymmetry. © 2006 Elsevier B.V. All rights reserved.