Searching for two-dimensional (2D) stable materials with direct band gap and high carrier mobility has attracted great attention for their electronic device applications. Using the first principles calculations and particle swarm optimization (PSO) method, we predict a new 2D stable material (HfN2 monolayer) with the global minimum of 2D space. The HfN2 monolayer possesses direct band gap (～1.46 eV) and it is predicted to have high carrier mobilities (～103 cm2·V?1·s?1) from deformation potential theory. The direct band gap can be well maintained and flexibly modulated by applying an easily exteal strain under the strain conditions. In addition, the newly predicted HfN2 monolayer possesses good thermal, dynamical, and mechanical stabilities, which are verified by ab initio molecular dynamics simulations, phonon dispersion and elastic constants. These results demonstrate that HfN2 monolayer is a promising candidate in future microelectronic devices.