A spread spectrum clock generating apparatus is disclosed. The spread spectrum clock generating apparatus includes a phase lock loop module and a spread spectrum module. The phase lock loop module is used for dynamically tuning frequency of an output clock. The spread spectrum module includes a counter, a plurality of delta-sigma counters and a data shifter. These delta-sigma counters accumulate input signals, and enable a first overflow signal while accumulation of a last stage delta-sigma counter is overflowed. The frequency of the output clock can be tuned dynamically according to the first overflow signal, and the spectrum of the output clock can be spread.