MgB2 superconductor has a great potential for applications because of its high Tc and Bc2, exceeding those of any Nb-base superconductors at any temperature. It is now important to understand its flux pinning so as to raise Jc to high values over a wide field range. We show that nanometer-sized columnar-grain structure can produce Jc exceeding 5×106 A/cm2. The angular dependence of Jc indicates that the strongest pinning occurs when the field is aligned parallel to the grain boundaries. Our results confirm earlier deductions that grain boundaries in MgB2 act as effective pinning centers like those in Nb3Sn.