Compared with a flat fingerprint, the rolled fingerprint has a larger fingerprint area and can be extracted more minutiae. It has high requirements in many fields, not only in the military environment or the police field but also in many civil application fields. The challenge that has been troubled for a long time is that contact-based rolled fingerprint registration is easy to cause obvious distortion without human experts' supervision, which has a negative impact on fingerprint recognition performance. Due to the elastic deformation of fingertips, the mosaicking gaps in the rolled fingerprint are usually visible but challenging to locate. To address these problems, we propose a novel rolled fingerprint construction algorithm called BlockRFC (Block-based Rolled Fingerprint Construction) in this paper. BlockRFC's core idea is to use the fingerprint image block as a processing unit for mosaicking and distortion rectification. BlockRFC is based on a real-time mosaicking framework, which makes it possible to construct a rolled fingerprint while collecting fingerprint images. One distinctive advantage of BlockRFC is that it does not require minutiae or ridge information, but fully utilizes the gray-scale information and foreground area in the fingerprint image block. In this paper, we first propose a metric called Mosaicking Gap Rate (MGR), which can effectively quantify the mosaicking gaps in the rolled fingerprints. Experimental results show that the proposed method can not only effectively locate and eliminate the mosaicking gaps but also have better recognition accuracy than previous methods.