This study formulates a stochastic nutrient-phytoplankton model which incorporates the effect of white noise on phytoplankton growth. The global existence and uniqueness of a positive solution, stochastic boundedness, and stochastically asymptotic stability are well explored. A stochastic ecological reproductive index R0s is formulated to characterize the global dynamics. The theoretical analysis demonstrates that, if R0s1 and some other conditions hold, then there exists an invariant and asymptotically stable density of the system and the approach involves integral Markov semigroups theory. Numerical simulations are presented to illustrate the analytical findings and to investigate the long-time effect of water temperature, light, nutrients, and environmental noise on the dynamic evolution of phytoplankton.