We present a new fast radix-3 algorithm for the computation of the length-N generalized discrete Hartley transform of type-II (GDHT-II), where N = 3^m, m ≥ 2. Then we apply this algorithm to the direct computation of length-N GDHT-II coefficients when given three adjacent length-N/3 GDHT-II coefficients. The computational complexity of the proposed method is lower than that of the traditional approach for length N ≥ 9. The arithmetic operations can be saved from 19% to 29% for N = 3^m varying from 9 to 243 and from 17% to 29% for N = 3×2^m varying from 12 to 384. Furthermore, the new approach can be easily implemented.