Satellite observations of the heliospheric current sheet indicate that the plasma flow velocity is low at the center of the current sheet and high on the two sides of current sheet. In this paper, we investigate the growth rates and eigenmodes of the sausage, kind, and tearing instabilities in the heliospheric current sheet with the observed sheared flow. These instabilities may lead to the formation of the plasmoids and kink waves in the solar wind. The results show that both the sausage and kink modes can be excited in the heliospheric current sheet with a growth time ∼ 0.05 5 day. Therefore, these modes can grow during the transit of the solar wind from the Sun to the Earth. The sausage mode grows faster than the kink mode for β ∞ < 1.5, while the streaming kink instability has a higher growth rate for β ∞ > 1.5. Here β ∞ is the ratio between the plasma and magnetic pressures away from the current layer. If a finite resistivity is considered, the streaming sausage mode evolves into the streaming tearing mode with the formation of magnetic islands. We suggest that some of the magnetic clouds and plasmoids observed in the solar wind may be associated with the streaming sausage instability. Furthermore, it is found that a large-scale kink wave may develop in the region with a radial distance greater than 0.5 1.5 AU.