Digital predistortion is one of the most widely used techniques to linearize a power amplifier (PA) to reduce the error vector magnitude (EVM) distortion and spectral regrowth. By far, the lookup table (LUT) predistorters are most frequently used scheme to mitigate the effects of non-linear power amplifier. In this paper, a new algorithm of joint-polynominal LUT predistorter which attains the best linearization performance is proposed. The algorithm employs the hermite interpolation LUT, which has a higher accuracy of interpolation. Simulation results show that the proposed method provides a better rejection of EVM distortion and an improvement of 30-40% of adjacent channel leakage ratio (ACLR) for the wideband code division multiple access at a minimal memory usage.