The invention provides a powder conveying and mixing device and a burner. The powder conveying and mixing device comprises a powder mixing pipe, a powder conveying pipe and a rotational flow strip, apowder mixing channel is arranged in the powder mixing pipe, and the powder conveying pipe is arranged at one end of the powder mixing pipe and is communicated with the powder mixing channel; and therotational flow strip spirally extends in the powder mixing channel around the center axis of the powder mixing pipe, the rotational flow strip and the powder conveying pipe are spaced in the axial direction of the powder mixing pipe, and a plurality of tooth openings are formed in the rotational flow strip. According to the powder conveying and mixing device, the rotational flow strip with the multiple tooth openings is arranged in the powder mixing channel, the swirling intensity of powder particles at an outlet of the powder conveying and mixing device can be guaranteed, the turbulent mixing intensity of the powder particles and carried air flow in the powder mixing channel is obviously improved, the uniform distribution character of the powder particles at the outlet of the powder conveying and mixing device can be improved.