Solar activity during 2008 - 2009 was extremely low among several recent solar cycles, raising an interesting question regarding the temporal and spatial distribution of the plasma parameters in ionosphere during this time period. This study analyzes the electron density (N_e) data recorded by the DEMETER satellite at the height of 670 km and compares it with the International Reference Ionosphere (IRI) 2007 model with special emphasis on the solar minimum year of 2008. The results show that in local nighttime around 22:30 the global distribution of N_e by the DEMETER satellite exhibited similar behavior as that by IRI model, but N_e is overestimated above 100% by the IRI in equatorial and beyond geomagnetic latitudes of 50°, while underestimated by -70% at 20° - 40° in the north or south hemisphere during different seasons. In local daytime around 10:30, N_e values are mostly overestimated by the IRI model especially in the equatorial area where double crests were exhibited clearly at ±10° in the IRI-N_eQuick model, but only one crest around 0° - 10°N shown by DEMETER. Combined with other satellite data double crests of N_e over the equatorial area may gradually evolve into a single peak near LT 10:30 at 600 km height. The DEMETER comparison with three options in IRI 2007 revealed that only the IRI-2001 option gave a single crest as with DEMETER, and three IRI options all largely overestimated the crest N_e values from DEMETER in local daytime. The results in this paper provide new information for improving the IRI model in the future, helping to understand the ionosphere and upper atmosphere physics, with applications in communications, navigation and spacecraft orbit determination.