There are disclosed a driving circuit of an organic light emitting display panel and an organic light emitting display apparatus. The driving circuit comprises: a power supply detection circuit configured to detect an operating state of an external input power supply, send a normal signal of power supply detection when it is determined that the external input power supply is in a normal state, and send a abnormal signal of power supply detection when it is determined that the external input power supply is in an abnormal state; a clock control circuit configured to convert a received video data into image data recognizable by the organic light emitting display panel and then output it to the organic light emitting display panel when the normal signal of power supply detection sent by the power supply detection circuit is received, and output image data of black picture to the organic light emitting display panel when the abnormal signal power supply detection sent by the power supply detection circuit is received. In this way, pixel charges accumulated on respective display pixels can be released, which avoids transistors inside the display pixels from producing stress, and finally avoids occurrence of shutdown image sticking due to power-down.