In this paper, we first establish a Landau-Bloch type theorem for certain bounded and normalized biharmonic mappings F(z) = |z| 2 (z) + h(z), where (z) and h(z) are harmonic in the unit disk with |(z)| ≤ M 1 , |h(z)| ≤ M 2. In particular, our result is sharp when M 1 = M 2 = 1. Then, we establish several new versions of Landau-Bloch type theorems for certain normalized biharmonic mappings with the coefficients condition in place of |h(z)| ≤ M 2 or |(z)| ≤ M 1 , and obtain several sharp results.