Physically unclonable functions (PUFs) have been a hot research topic in hardware-oriented security for many years. Given a challenge as an input to the PUF, it generates a corresponding response, which can be treated as a unique fingerprint or signature for authentication purpose. In this paper, a delay-based PUF design involving multiplexers on FPGA is presented. Due to the intrinsic difference of the switching latencies of two chained multiplexers, a positive pulse may be produced at the output of the downstream multiplexer. This pulse can be used to set the output of a D flip-flop to `1'. Further, it is proposed to directly incorporate challenge bits into the primitive PUF design to bring another layer of randomness for the response. Evaluation results on various devices and under different operating temperatures demonstrate the applicability of the proposed PUF design.