This paper presents a novel algorithm design of 18-band quasi-class-2 ANSI S1.11 1/3 octave filter bank with the advantages of low group delay and low complexity. The proposed method utilizes a simple low-pass filter (LPF) and discrete cosine transform (DCT) modulation to generate a uniform 9-band filter bank first, and then transfer all element of z-1 into all-pass filter in order to obtain the non-uniform filter bank to meet the standard. Additionally, a fast recursive DCT algorithm is proposed to efficiently accomplish variable-length modulation. Hence, the spectrum of LPF can be easily spanned and flexibly extended to the position of the desired central frequency. Finally, by combining with multi-rate concept, we can realize an 18-band quasi-class-2 filter bank design. Compared with the latest Liu et al.'s quasi-class-2 ANSI S1.11 design, the proposed method totally has 63.4% reduction for multiplications per sample and 14-ms group delay, although we still have 15.2% increase for additions per sample.