The utility model discloses a light emitting diode (LED) driving chip capable of dimming and a driving circuit, which belong to the fields of a driving chip and a driving circuit. The LED driving chip capable of dimming comprises a feedback pin, a voltage output pin, a grounding pin, a switching tube pin, a dimming control pin, a power voltage input pin, a switching tube, a logical driving module, a protecting circuit module, a dimming digital control module, an error amplifier, a pulse-width modulation (PWM) comparator and a band-gap reference voltage module. According to the LED driving chip capable of dimming and the driving circuit, a digital dimming mode is adopted, a PWM modulation signal is regulated by a digital dimming control signal, a sectional type dimming mode is adopted, the problem of electro-magnetic interference (EMI) under a traditional PWM dimming mode is solved, and the efficiency of a driving power supply is effectively enhanced. By selecting analog-digital converters with different bits, LED dimming modes with different accuracy can be realized. According to the LED driving chip capable of dimming and the driving circuit, the aim of full-power regulation is realized, and the requirements to a main circuit and a working mode under a peak current control mode are met.