We present the results on the searches for the SM and the non-SM
Higgs boson production in p anti-p collisions at s**(1/2) = 1.96 TeV with the CDF
detector at the Fermilab Tevatron. Using data corresponding to 300-700
pb-1, we search for the Higgs boson in various production and decay
channels. No signal is observed, therefore, we set upper limits on the
production cross-section times branching fraction as a function of the Higgs
boson mass.