We simulate the microphase separation dynamics of the triblock polymer surfactant (ethylene oxide)(19)(propylene oxide)(29)(ethylene oxide)(19) (P65) in aqueous solution by a dynamic variant of mean-field density functional theory for Gaussian chains. With the increase of concentration, different mesoscale structures are found in the absence and presence of shear. (1) In the absence of shear, there are three morphologies formed. The first is the micellar phase, including a spherical micelle, which has hexagonal packing and a fcc (face-centered cubic) structure in the solution and a wormlike micelle, the second is the bicontinuous phase, which belongs to gyroidtype connectivity, and the third is the lamellar phase. (2) In the presence of shear, only two morphologies are formed in all concentrations, they are hexagonal and lamellar phases, which align in the flow direction. We notice that the weak shear makes the order parameters of the simulation system oscillate, while the strong shear makes the order parameter get equilibrated in a short time. It is concluded that the mesoscopic simulation method is a valuable tool for description of mesoscale morphology formation in the absence or presence of shear and can give mesoscale information for the experiments.