This paper develops a one and two factor Adaptive Binomial Model (ABM) to price financial derivatives. By building several levels of finer trees around critical regions, the ABM improves upon the binomial model by significantly reducing pricing errors for all tree-based derivatives valuation. The improvement in efficiency should be in the order of $4^L$ with $L$ being the level of fine mesh employed. The model is applied to price several derivatives securities, e.g. discrete barrier options, knock-out swaps, and index knock-out bonds. For this class of derivatives, the pricing error comes mainly from the price discontinuity around the knock-out region. Numerical results show significant improvement in pricing accuracy. For the index knock-out bond, such improvement proves to be critical in getting an accurate price, because physical limitation of computer resources prevent us from getting an accurate price at all with the standard binomial model.