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We consider a locally rotationally symmetric (LRS) Bianchi type-Ⅱ spacetime with a perfect fluid and a variable cosmological constant ∧.To solve the Einstein field equations we consider the cosmological term ∧ to be proportional to R-m with R being the scale factor and m a constant [Phys.Rev.D 58 (1998) 043506].In this model we obtain ∧ ～ H2,∧ ～ (R)/R and Labda ～ t-2,in agreement with the main dynamical laws for the decay of ∧.The physical significance of the cosmological model is also discussed.