An abundance estimation algorithm based on orthogonal bases is proposed to address the problem of high computational complexity faced by most abundance estimation algorithms that are based on a linear spectral mixing model (LSMM) and need to perform determinant operations and matrix inversion operations. The proposed algorithm uses the Gram-Schmidt method to calculate the endmember vector set to obtain the corresponding orthogonal basis set and solve the unmixing equations to obtain the eigenvector of each endmember. The spectral vector to be decomposed is projected onto the eigenvector to obtain projection vector, and the ratio between the length of the projection vector and the length of the orthogonal basis corresponding endmember is calculated to obtain an abundance estimation of the endmember. After a comparative analysis of different algorithms, it is concluded that the proposed algorithm only needs to perform vector inner product operations, thereby significantly reducing the computational complexity. The effectiveness of the algorithm was verified by experiments using simulation data and actual image data.