Hi , I was checking the gear ratio transfer case Samurai, which multiplies in HI and LOW, my question is possible putting on a transfer case samurai to a Vitara and Grand Vitara 2002 4 Doors , Automatic, 2.0 engine ?

It's not a bolt on swap, but as far as I know, it can be done.

Essentially you remove the transfer case from the back of the transmission and fit an adapter to take the jack shaft to the Samurai transfer case (Low Range Off Road should have the adapters) - you will need to fabricate transfer case mounts, new drive shafts, etc., etc., etc., the new rear drive shaft may need a CV joint (or double cardans) because the rear drive shaft will be at a compound angle (the GV rear axle has the diff in the center, the Samurai transfer case output shaft is offset to the right).

Have you considered replacing the axle gears - it might work out less expensive, it'll certainly be a lot less fabrication.

X2 on increasing the diff gearing in your axles and/or just adding transfer case gears to your existing transfer case.  These would be more straight forward and less complicated increases for improving your gearing.

Thanks for your answers , I go first with lockright in the rear differential just concerned that drive me daily in the city and weekends in the field.

I've run a Lock Right in the back of my '02 Tracker (think GV) since about November 2011... or for about 60K miles now and honestly, the Lock Right hasn't presented any issues that make me ever regret installing it. 

During my diff rebuild last year, I installed a Lock Right rebuild kit in the Locker (new pins and spring kit) and also installed the smooth shaft hardened cross pins (had made in a local tool shop).  The Lock Right in my truck has been even smoother and more predictable than before.  My wife now drives my Tracker occasionally because she now thinks it drives better and more predictably than before.

I have a manual transmission though, so I can unload the torque off my drive train a little easier during turns than an automatic transmission equipped truck would.

Excellent news , tell me the model you have installed lockright to buy it.

The Lock Right I run in my Tracker is a #1512LR.

Be sure to coat all the thrust washers, gears, pins and springs with grease during assembly.  Helps to keep all the parts lubed initially before the gear oil gets down into all the surfaces.  The pins go into the oblong holes (yes... I was talking too much and not paying attention to what I was doing during one install).  You will use all eight springs in the kit.  The smaller springs nest inside the slightly larger springs and they sit into the perfectly round holes and then the pins sandwich into the spring pockets during assembly.  As usual, mark your diff carrier parts (with a punch) and take note of the number of threads on the side bearing nuts that are visible before disassembly to ensure a proper reassembly.

Thanks