A new high-accuracy current-mode function generator circuit will be presented, the proposed computational structure being designed for implementing a multitude of circuit functions with many applications in VLSI designs. The realization of the original function generator is based on the utilization of a new third-order approximation function that allows to strongly reduce the approximation error for the implemented functions. The circuit requires a much smaller silicon area comparing to similar previouslys reported circuits. The current-mode operation and the independence of the output current of the function generator on technological parameters and on temperature variations additionally increase the overall circuit accuracy. The simulations confirm the theoretical estimated results, showing an accuracy of the functional squaring core equal with 0.97 %. The new proposed function generator based on the third-order approximation function permits to obtain a wide output dynamic range of 28dB for a maximal error of 1dB, when implementing the exponential function. The proposed function generator is designed for a low-voltage operation, being supplied at V-DD=1V.