The invention relates to a repair method of an elevator provided with a car roof fairing and the elevator achieving the method. The repair method of the elevator comprises the fairing separation steps that the car roof fairing is kept at a preset position in a well; a car is driven to move downwards; and the car roof fairing is separated from the car accordingly. The upper portion of the car roof fairing can also be separated from the car. The elevator achieving the method is provided with brackets (136) mounted on car guide rails (122) and supporting arms (126) which are arranged on the upper portion of the car roof fairing and are capable of stretching towards the brackets to be erected to the brackets so as to enable the brackets to bear the upper portion (114a) of the car roof fairing. The upper portion of the car roof fairing is detachably and fixedly connected with the lower portion (114b) of the car roof fairing, and when the upper portion of the car roof fairing is disconnected from the lower portion of the car roof fairing, the supporting arms are erected to the brackets, the car (110) is driven to move downwards, and the upper portion of the car roof fairing can be separated from the car. In this way, obstacle of the car roof fairing to repair operation can be eliminated.