Current Network Function Virtualization (NFV) with Virtualized Network Functions (VNFs) running as virtual machines on commodity servers enables flexibility to Service Function Chaining (SFC). Specific applications may require Quality of Service (QoS) on end-to-end latency. However, the processing delay and the queuing delay of VNFs varies with virtual resource configurations (vCPU and vMemory), as well as physical usage (traffic amount, CPU utilization). Moreover, packet delays are randomly distributed, instead of a fixed value. To accurately model the latency distribution of one VNF, a prediction method using random-forest regression is proposed. Evaluation results show that our method can predict the latency distribution of the two sample VNFs with only 10% errors. On the basis of the model, a QoS-assured SFC deployment algorithm is also presented to guarantee end-to-end latency and bandwidth consumption of users. Experiments show that our algorithm enables high degree of scalability with polynomial runtime, and meanwhile maximizes user acceptance rates with 6% difference from the optimal solution from the mixed integer programming.