Graphical models have become a useful approach to studying the interactions between microbial taxa from microbiome data. Recently, various methods for sparse inverse covariance estimation have been proposed, such as graphical lasso, for graphical models. However, current methods do not address the compositional count nature of microbiome data, where abundances of microbial taxa are not directly measured but are presented by error-prone counts. Adding to the challenge is that the sum of the counts within each sample, termed "sequencing depth", can vary drastically across samples. To address these issues, we adopt a multinomial log-normal model explicitly incorporating the sequencing depth, and develop an algorithm via block coordinate descent for model estimation. We call this new method "compositional graphical lasso." We show that our algorithm converges to a local optimum and the resulting estimator possesses nice properties. Additionally, we will illustrate the advantage of our method under a variety of simulation scenarios and in an application to human microbiome data.