We present a practical laser linewidth broadening phenomenon in the viewpoint of high sensitivity of an exceptional point (EP). A stochastic simulation model is implemented to describe the fluctuations in the cavity resonance frequencies. The linewidth originated from external noises are maximized at the EP. The linewidth enhancement factor behaves similarly to the Petermann factor although the Petermann effect is not considered. In the long coherence time limit, the power spectral density of the laser exhibits a splitting in the vicinity of the EP although the cavity eigenfrequencies coalesce at the EP.