We extend our previous perturbative study of the multiphoton detachment of H [Phys. Rev. A 48, 4654 (1993)]to stronger fields by considering the intensity-dependent photodetachment rates and threshold behavior. An accurate one-electron model potential, which reproduces exactly the known H binding energy and the low-energy e-H(1s) elastic-scattering phase shifts, is employed. A computational technique, the complex-scaling generalized pseudospectral method, is developed for accurate and efftcient treatment of the time-independent non-Hermitian Floquet Hamiltonian PF. The method is simple to implement, does not require the computation of potential matrix elements, and is computationally more e5cient than the traditional basis-set-expansion-variational method. We present detailed nonperturbative results of the intensity-and frequency-dependent complex quasienergies (E&, -I /2), the complex eigenvalues of Pr, providing directly the ac Stark shifts and multiphoton detachment rates of H The laser intensity considered ranges from 1 to 40 GW/cm2 and the laser frequency covers 0.20-0.42 eV (in the c.m. frame). Finally we perform a simulation of intensity-averaged multiphoton detachment rates by considering the experimental conditions of the laser and H beams. The results (without any free parameters) are in good agreement with experimental data, both in absolute magnitude and in the threshold behavior. PACS number(s): 32.80. Rm, 32.80.Fb, 42.50.Hz