We constructed a time-dependent, three-dimensional, multi-ion numerical model of the global ionosphere at F region altitudes. The model takes account of all the processes included in the existing regional models of the ionosphere. The inputs needed for our global model are the neutral temperature, composition, and wind; the magnetospheric and equatorial electric field distributions; the auroral precipitation pattern; the solar EUV spectrum; and a magnetic field model. The model produces ion (NO+ O+2,N+2, N+, O+, He+) density distributions as a function of time. For our first global study, we selected solar maximum, low geomagnetic activity, and June solstice conditions. From this study we found the following (1) The global ionosphere exhibits an appreciable UT variation, with the largest variation occurring in the southern winter hemisphere; (2) At a given time, NmF2 varies by almost three orders of magnitude over the globe, with the largest densities (5¿106 cm-3) occurring in the equatorial region and the lowest (7¿103 cm-3) in the southern hemisphere mid-latitude trough; (3) Our Appleton peak characteristics differ slightly from those obtained in previous model studies owing to our adopted equatorial electric field distribution, but the existing data are not sufficient to resolve the differences between the models; (4) Interhemispheric flow has an appreciable effect on the F region below about 25¿ magnetic latitude; (5) In the southern winter hemisphere, the mid-latitude trough nearly circles the globe. The dayside trough forms because there is a latitudinal gap of several degrees between the terminator and the dayside oval. In this gap, there is no strong ion production source, and the ionosphere decays; (6) For low geomagnetic activity, the effect of the auroral oval on the densities is not very apparent in the summer hemisphere, but is clearly evident in the winter hemisphere; (7) The densities in both the northern and southern polar caps exhibit a complex temporal variation owing to the competition between the various photochemical and transport processes.