After getting new front brake pads my car braking power is just amazing. I can slightly step on the brake and I can feel the brake engage and would stop the car with out having to step on the brake really hard.

After the brake pads are about half way used, I have to really step on the brake pedal really hard to stop the car.

What could be wrong with my brake?

 

Sounds like a master cylinder issue. Start by checking the fluid level and the color.

 

Depending on how far your pedal has to travel when you apply the brakes you could have air in the system. After you check the fluid level/color and if they're fine or a little low, bleed the brakes and top it off with fresh fluid and see if that helps.

 

The throw of the master cylinder piston, or how much the pedal depresses, is constant.
Only times this would change if the rear brake self adjusters seize requiring more and more pedal travel as the rear pads/shoes wear and fully retract. This will require more pedal travel, or from a leak.

If the problem seems to occur after when the pads wear to a certain point then it is most likely a problem with the caliper pins sliding(gummed up, worn or bent) or varnish/corrosion built up on the piston of the caliper. I would suspect there is a buildup on the pistons, and when the piston tries to expand past the seal of the caliper(not the dust boot) there is a build up of corrosion/junk on the piston that prevents the piston from easily sliding past the seal at this point. This would occur if the brake fluid has not been regularly flushed/changed and the pads were changed earlier than needed, thus the piston never 'wipes' past that seal at a given depth allowing buildup and requiring more pedal force to move the piston past the seal.