Using the Luminous Red Galaxy (LRG) sample of the SDSS Data Release 6, we investigate the dependence of LRG properties on the local environment. For each LRG, the local three dimensional density within the distance to the 5th nearest galaxy is calculated. It turns out that there is no strong local environmental dependence of LRG morphologies, and that other galaxy properties do not present significant dependence on the local environment. We further calculate the local three dimensional galaxy density within the distance to the 10th nearest galaxy, and find that results are similar to those for local density within the distance to the 5th nearest galaxy.