We would study compactness via grills in a neutrosophic topological space. We call it neutrosophic weak \(\mathscr {G}\) -compactness. We would investigate some basic properties and characterization theorems of it. We would also obtain its relationship with other known neutrosophic compactness. Lastly, we would exhibit and study neutrosophic weak compactness through neutrosophic \(\theta \) -open sets.