We have developed a new 3-dimensional climate model for Titan’s atmosphere, using the physics of the IPSL Titan 2-dimensional climate model with the current version of the LMDZ General Circulation Model dynamical core. Microphysics and photochemistry are still computed as zonal averages. This GCM covers altitudes from surface to 500 km altitude, with barotropic waves now being resolved and the diurnal cycle included. The boundary layer scheme has been changed, yielding a strong improvement in the tropospheric zonal wind profile modeled at Huygens descent position and season. The potential temperature profile is fairly consistent with Huygens observations in the lowest 10 km. The latitudinal profile of the near-surface temperature is close to observed values. The minimum of zonal wind observed by the Huygens probe just above the tropopause is also present in these simulations, and its origin is discussed by comparing solar heating and dynamical transport of energy. The stratospheric temperature and wind fields are consistent with our previous works. Compared to observations, the zonal wind peak is too weak (around 120 m/s) and too low (around 200 km). The temperature structures appear to be compressed in altitude, and depart strongly from observations in the upper stratosphere. These discrepancies are correlated, and most probably related to the altitude of the haze production. The model produces a detached haze layer located more than 150 km lower than observed by the Cassini instruments. This low production altitude is due to the current position of the GCM upper boundary. However, the temporal behaviour of the detached haze layer in the model may explain the seasonal differences observed between Cassini and Voyager 1. The waves present in the GCM are analyzed, together with their respective roles in the angular momentum budget. Though the role of the mean meridional circulation in momentum transport is similar to previous work, and the transport by barotropic waves is clearly seen in the stratosphere, a significant part of the transport at high latitudes is done all year long through low-frequency tropospheric waves that may be baroclinic waves.