MRI of laser-polarized $^{129}$ Xe under continuous flow conditions has recently been used for imaging of porous materials, however, any attempts at using a continuously circulating flow of laser-polarized $^3$He have not been made until now, presumably due to its extremely long spin exchange time (5-10 hrs). Since the inherent NMR sensitivity of $^3$He is 80 times greater than that of $^{129}$ Xe when considering the natural abundance, $^3$He can be expected to be a better nucleus for imaging than $^{129}$ Xe even under continuous flow conditions. In this report, the first MRI with continuously flowing laser-polarized $^3$He is shown for a phantom of Teflon tubing, demonstrating the feasibility of $^3$He imaging under continuous flow.