Using the polar decomposition of a bounded linear operator A defined on a complex Hilbert space, we obtain several numerical radius inequalities of the operator A, which generalize and improve the earlier related ones. Among other bounds, we show that if w(A) is the numerical radius of A, then [Formula presented] for all t∈[0,1]. Also, we obtain some upper bounds for the numerical radius involving the spectral radius and the Aluthge transform of operators. It is shown that [Formula presented] where A˜=|A|1/2U|A|1/2 is the Aluthge transform of A and A=U|A| is the polar decomposition of A. Other related results are also provided.