We demonstrate the first diode-pumped Ti:sapphire laser frequency comb. It is pumped by two green laser diodes with a total pump power of 3 W. The Ti:sapphire laser generates 250 mW of average output power in 61-fs pulses at a repetition rate of 216 MHz. We generated an octave-spanning supercontinuum spectrum in a photonic-crystal fiber and detected the carrier envelope offset (CEO) frequency in a standard f-to-2f interferometer setup. We stabilized the CEO-frequency through direct current modulation of one of the green pump diodes with a feedback bandwidth of 55 kHz limited by the pump diode driver used in this experiment. We achieved a reduction of the CEO phase noise power spectral density by 140 dB at 1 Hz offset frequency. An advantage of diode pumping is the ability for high-bandwidth modulation of the pump power via direct current modulation. After this experiment, we studied the modulation capabilities and noise properties of green pump laser diodes with improved driver electronics. The current-to-output-power modulation transfer function shows a bandwidth larger than 1 MHz, which should be sufficient to fully exploit the modulation bandwidth of the Ti:sapphire gain for CEO stabilization in future experiments.