Field equations of undefined theory of gravity are obtained with the aid of locally rotationally symmetric (LRS) Bianchi type-I metric when the matter source is a bulk viscous fluid containing one dimensional cosmic strings. Applying some physically possible conditions, we have obtained a determinate solution of the field equations. The deceleration parameter of our model exhibits a smooth transition from early decelerated phase to late time accelerating phase. We also find that the realistic energy conditions p ≥ 0 and pp ≤ 0 are satisfied in our model. Some other properties of the model are also discussed.