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 $N = 3\times 2 ^{ m}$ varying from 12 to 384. Furthermore, the new approach can be easily implemented.