Two-dimensional particle-in-cell simulations show that when an intense picosecond laser pulse irradiates a target with steep but smooth density profile, the target protons can be accelerated to high energies with small divergence by a combination of target normal sheath acceleration and radiation pressure acceleration. The effects of plasma density profile on proton acceleration and collimation are investigated. In general, smaller(larger) density gradients lead to larger(smaller) self-generated azimuthal magnetic fields and smaller(larger) target-back electrostatic sheath fields, and thus proton beams with smaller(larger) divergence angle as well as cutoff energy. Accordingly, within limits, proton beams with desired peaked spectrum, energy, and divergence angle can be obtained by tailoring the target density profiles. It is also demonstrated that target tailoring can be achieved by having two suitable nanosecond lasers separately irradiating the front and back sides of a uniform plane slab.