Constructing gene regulatory networks is a critical step in revealing disease mechanisms from transcriptomic data. In this work, we present NO-BEARS, a novel algorithm for estimating gene regulatory networks. The NO-BEARS algorithm is built on the basis of the NO-TEARS algorithm with two improvements. First, we propose a new constraint and its fast approximation to reduce the computational cost of the NO-TEARS algorithm. Next, we introduce a polynomial regression loss to handle non-linearity in gene expressions. Our implementation utilizes modern GPU computation that can decrease the time of hours-long CPU computation to seconds. Using synthetic data, we demonstrate improved performance, both in processing time and accuracy, on inferring gene regulatory networks from gene expression data.