Why does the sun have higher pressure in the core? Isn't the gravity increases linearly with the radius and highest pressure on the surface?

Notice that the sun is a sphere of GAS, not solid.

Gravity pulls the gas (hydrogen) molecules inward into the centre. As such, the density of molecules (i.e. no. of molecules per unit volume) towards the centre is much much higher than that on the surface. This gives rise to a higher pressure at the centre of the sun.

The situation is similar to that on earth. Gravity on earth tends to pull air molecules downward towards earth surface. This results that the air pressure on earth surface (or pressure at sea level) is higher than pressure at top of mountains.