To investigate the effects of wave shape on cohesive sediment flux in shallow water environments, a one-dimensional vertical (1DV) model for cohesive sediment transport previously validated with field measurement is applied to conditions of skewed and asymmetric oscillatory flows. Cohesive sediments usually portray behaviors different from those of noncohesive sediments. This is mainly due to the flocculation process through which the density and the size of cohesive sediment change continuously. Therefore, a robust flocculation model is incorporated with a 1DV model in this study. Under the condition of skewed oscillatory flow (second-order Stokes wave-type oscillatory flow), the flux of cohesive sediment is significantly affected by the change of flow skewness, whereas the flux of noncohesive sediment of which size is 100 µm does not show a clear relationship with skewness. Under the condition of forward-leaning asymmetric oscillatory flow (saw-tooth wave-type oscillatory flow), the direction of cohesive sediment flux is negative, whereas the flux of noncohesive sediment shows the positive direction. The phase-lag effect is considered as the main mechanism of these behaviors. The interactional relationship between the settling velocity, the variation of concentration profile, and hydrodynamics of carrier fluid enhances the phase-lag effect and causes different behaviors in cohesive sediment compared to the flux of fine noncohesive sediment.