We propose a computing method for linear convolution and linear correlation between sequences using discrete cosine transform (DCT). Zero-padding is considered as well as linear convolution using discrete Fourier transform (DFT). Analyzing the circular convolution between symmetrically extended sequences, we derive the condition for zero-padding before and after the sequences. The proposed method can calculate linear convolution for any filter and also calculate linear correlation without reversing one of the input sequences. The computational complexity of the proposed method is lower than that of linear convolution using DFT.