Euler deconvolution is a popular technique used for analyzing potential field data because it requires little prior information. However, the reliability of Euler solutions can be impacted by interference from adjacent field sources, or background fields. In this manuscript, we present an effective Euler deconvolution algorithm that accounts for linear background fields. Our algorithm, called improved finite-difference Euler deconvolution, builds upon the finite-difference method and is less susceptible to interference from nearby sources. We use this algorithm to achieve a joint estimation of the coefficients of the source coordinates, the structure index, and the linear background trend. Compared to Euler deconvolution methods based on differential similarity transformations, which also account for linear background fields, our method is easier to understand and implement programmatically and is faster. We tested our method using both 2D and 3D synthetic data, and the results indicate that our algorithm has better computational accuracy than the finite-difference algorithm and is comparable to the Euler deconvolution algorithm based on differential similarity transformations. In addition, our method was shown to be effective when tested on real data.