A nuclear reactor cooling system with passive cooling capabilities operable during a reactor shutdown event without available electric power. In one embodiment, the system includes a reactor vessel with nuclear fuel core and a steam generator fluidly coupled thereto. Primary coolant circulates in a flow loop between the reactor vessel and steam generator to heat secondary coolant in the steam generator producing steam. The steam flows to a heat exchanger containing an inventory of cooling water in which a submerged tube bundle is immersed. The steam is condensed in the heat exchanger and returned to the steam generator forming a closed flow loop in which the secondary coolant flow is driven by natural gravity via changes in density from the heating and cooling cycles. In other embodiments, the cooling system is configured to extract and cool the primary coolant directly using the submerged tube bundle heat exchanger.