We present the measurement of ttbar production cross section using L = 110 pb^-1 data sample of ppbar collisions at sqrt s = 1.8 TeV collected with the Collider Detector at Fermilab (CDF). Combining the results from the channels with at least one W decaying into leptons (e or mu) plus jets we measure sigma_ttbar = 7.5^1.9_ -1.6 pb. We report the observation of ttbar production in the all hadronic decay channel using a kinematical selection and b identification techniques. Finally we show preliminary evidence for ttbar production in the decay mode with one e or mu in the final state and an hadronically decaying tau.