This article is dedicated to investigating the impulsive-based almost surely synchronization issue of neural network systems (NSSs) with quality-of-service constraints. First, the communication network considered suffers from random double deception attacks, which are modeled as a nonlinear function and a desynchronizing impulse sequence, respectively. Meanwhile, the impulsive instants and impulsive gains are randomly and only their expectations are available. Second, by taking two different types of random deception attacks into consideration, a novel mathematical model for vulnerable NSSs is constructed. Then, almost surely synchronization criteria are established by using Borel-Cantelli lemma. Furthermore, based on the derived strong and weak sufficient conditions, the almost surely synchronization of NSSs is achieved. Finally, the section of numerical example is shown to illustrate the effectiveness of the proposed method.