High-precision microwave spectroscopy has been used to measure the transition frequency of nS1/2 → nPJ (n is the principle quantum number) and further the quantum defect of nPJ states in a standard cesium magneto-optical trap. A microwave field with 30-μs duration coupling the nS1/2 → nP1/2,3/2 transition yields a narrow linewidth microwave spectroscopy with the linewidth approaching the Fourier limit. After carefully compensating the stray electric and magnetic field and using the diluted atomic gas, we extract improved quantum defects of nPJ state, δ0(nP1/2) = 3.59159091(19), δ2(nP1/2) = 0.36092(35) and δ0(nP3/2) = 3.55907153(25), δ2(nP3/2) = 0.37344(47).