A model of a cloud formed by massive strings is used as a source of LRS Bianchi type-II with time-decaying vacuum energy density 𝛬. To construct string cosmological models, we have used the energy–momentum tensor for such strings as formulated by Letelier (1983). The high nonlinear field equations have been solved for two types of strings: (i) massive string and (ii) Nambu string. The expansion 𝜃 in the model is assumed to be proportional to the shear 𝜎. This condition leads to $A = \beta B^m$, where 𝐴 and 𝐵 are the metric coefficients, 𝑚 is a constant and 𝛽 is an integrating constant. Our models are in accelerating phase which is consistent with the recent observations of supernovae type-Ia. The physical and geometrical behaviour of these models are also discussed.