This paper presents an efficient constant-time Gaussian filter which provides a high accuracy at a low cost over a wide range of scale σ. It requires only 14 multiplications per pixel in image filtering regardless of σ, which is fewer than state-of-the-art constant-time Gaussian filters. Main ideas of the paper are as follows: 1) introducing a second-order shift property of the discrete cosine transform type-5 (DCT-5) to convolve cosines faster, and 2) suppressing error propagation caused by the shift property. Experiments in image processing show that the proposed algorithm is 3.7× faster than a state-of-the-art recursive Gaussian filter and comparable to that of ±3σ-supported Gaussian convolution with σ = 2.33. The output accuracy is stable at around 80 [dB] all over σ [1, 128].