The protein has some basal expression prior to induction which you are seeing in unindexed. It must be low expression (what you are seeing), but post induction there will be a marked difference in band intensity. if you want to get rid of the protein in uninduced sample you could try induction at an earlier time point than what you are currently doing. Also, monitoring the OD of your culture could give you an idea of the stage of cell growth. Try to induce when OD is 0.4 (early log phase). 

I have added IPTG at different time points( 1h, 1.5h, 2h, 2.5h) but I am seeing the same result in all. The intensity of uniduced is more than induced.

If your construct was stored as glycerol stock of expression host then it might not work as recA positive expression hosts do not stably retain plasmid vectors. Please retransform expression bacteria.

Some tryptones and, of course, casein hydrolysates) have enough residual lactose to produce spontaneous induction in LacY+ hosts such as BL21(DE3) (See the original Studier paper on autoinducing media and references thereof). If you are using LB or something similar, try adding glucose at 0.5% to the medium and do not allow the cells to reach stationary phase at any stage of the seeding train.

How did you get the new batch of cells growing? If you just put the -80 stock right into liquid culture you could have overgrowth of recombinats with deleted inserts (especially if the gene product is toxic). Can do a DNA minprep and RE digestion to check for insert. I normally streak on a new plate and pick a fresh colony to start up a new culture from a -80 stock. Also, how old is your IPTG?, it is temp. and light sensitive, and is your antibiotic freshly made?. Do you have a control cell line with non-toxic protein expression to check you reagents?