I have developed code for k-e model and it is applied for square lid driven cavity for Re=480000. it is working well, and when it is for rectangular cavity with x:y 1:3, it is not giving good results. I will be thankful if can anybody suggest me regarding this.

Some instability of the large-scale flow may develop. In this case your RANS method may become too inaccurate. Even in the square case, the small-scales of corner flow calculated seems OK?

Does any alternative is there to overcome this...

I am not quite sure how to improve a RANS scheme, add more Numerical Viscosity to suppress those instabilities or reduce NV to model. A more accurate model may work, but that type of instability is more subtle and probably inherent in the flow itself.