Recent advancements in spatial transcriptomic technologies have enabled the measurement of whole transcriptome profiles with preserved spatial context. However, limited by spatial resolution, the measured expressions at each spot are often from a mixture of multiple cells. Computational deconvolution methods designed for spatial transcriptomic data rarely make use of the valuable spatial information as well as the neighboring similarity information. Here, we propose SONAR, a Spatially weighted pOissoN-gAmma Regression model for cell-type deconvolution with spatial transcriptomic data. SONAR directly models the raw counts of spatial transcriptomic data and applies a geographically weighted regression framework that incorporates neighboring information to enhance local estimation of regional cell type composition. In addition, SONAR applies an additional elastic weighting step to adaptively filter dissimilar neighbors, which effectively prevents the introduction of local estimation bias in transition regions with sharp boundaries. We demonstrate the performance of SONAR over other state-of-the-art methods on synthetic data with various spatial patterns. We find that SONAR can accurately map region-specific cell types in real spatial transcriptomic data including mouse brain, human heart and human pancreatic ductal adenocarcinoma. We further show that SONAR can reveal the detailed distributions and fine-grained co-localization of immune cells within the microenvironment at the tumor-normal tissue margin in human liver cancer.