Self-Shielded axial gradient coils for eddy-current-free NMR imaging and spectroscopy have been designed using the target field approach proposed by Turner, Mansfield and Chapman. Optimal radius for the target field was determined to eliminate the additional resistors which may degrade the transient shielding performance. The magneic fields generated by the designed coils were calculated using Fourier-Bessel expansion, showing that the coils produce highly linear gradients and very small residual external fields.