This brief paper presents some bounds of coefficients of Daubechies orthonormal wavelets. For a nonnegative integer \(k\), let \(\phi_m^D\) be a Daubechies orthonormal wavelet of order \(m\) with \(m>k\). It is shown that for any \(p>1\), constants \(C_1\), \(C_2>0\) and \(0<\varepsilon<\pi\), the \(p\)-norm of the \(k\)-th coefficient \(\phi_m^D\) is bounded by two constants, both of which are functions of \(p\), \(k\), \(m\), \(C_1\), and \(C_2\). The expressions of these two bounds have been worked out exactly.