A pulverized coal burner and a pulverized coal boiler. The coal burner comprises a primary air cylinder (111) and a pulverized coal concentration device (112). The coal concentration device (112) makes the concentration of the coal flow gradually decrease from inside to outside along the radial direction, with respect to an axis (100) of the primary air cylinder (111). The coal burner further comprises a coal separating cylinder (113) and a coal guiding cylinder (114) located downstream of the device (112), the rear end of the cylinder (113) is connected with the front end of the coal guiding cylinder (114). The outlet of the cylinder (114) has a conical expansion portion (1141). The coal burner further comprises a divergent nozzle (115) connected with the rear end of the primary air cylinder (111) and whose cross-sectional area gradually increases along the flow direction of the coal flow.