Summary: The double generalized linear models (DGLM) allow the fit of the dispersion parameter of the response variable as a function of explanatory variables. Thus they are a possible solution when the assumption of constant dispersion parameter is unreasonable and the response variable follows a distribution from the exponential family. As in other classes of regression models, variable selection is an important step in the fit of a DGLM. In this work, we propose the \(k\)-steps variable selection scheme in double generalized linear models, where \(k\) is the number of steps required to achieve convergence. To check the performance of our procedure, we performed Monte Carlo simulation studies. The results indicate that our procedure for variable selection presents, in general, similar or superior performance than the other studied methods without requiring a large computational cost. We also evaluated the \(k\)-steps variable selection scheme using real data. The results suggest that our procedure can also be a good alternative when prediction is the main goal of the model.