Studies have been conducted using the ion-beam-gas excitation method with a doubly differentially pumped gas target (with a pressure ratio of 104 to 1 or more between gas target and observation chamber) to obtain the first known radiative-lifetime measurements for the 3p 5P (3849 Å), 3p 3P (4025 Å), 3d 5D0 (3504 Å), 3p'3D (4114 Å), 3p'1F (4299 Å), and 3p'3F (3901 Å) levels of F II. The lifetimes of these levels were measured as 8.17+/-0.29, 8.18+/-0.24, 5.74+/-0.20, 10.62+/-0.08, 10.41+/-0.68, and 9.45+/-0.34 ns, respectively. In addition, the lifetime associated with 3602-Å F II transition was measured as 4.40+/-0.27 ns, the level (s) of origin being undetermined (either 3p''3P or 3d'3G0). The uncertainties given are two times the standard deviations of the means (~95% confidence level). Absolute uncertainties are estimated to be less than 10%.