This paper is associated to investigate a stochastic SEIAQHR model for transmission of Coronavirus disease 2019 that is a recent great crisis in numerous societies. This stochastic pandemic model is established due to several safety protocols, for instance social-distancing, mask and quarantine. Three white noises are added to three of the main parameters of the system to represent the impact of randomness in the environment on the considered model. Also, the unique solvability of the presented stochastic model is proved. Moreover, a collocation approach based on the Legendre polynomials is presented to obtain the numerical solution of this system. Finally, some simulations are provided to survey the obtained results of this pandemic model and to identify the theoretical findings.