Manipulation of flowering time to develop cultivars with desired maturity dates is fundamental in plant breeding. It is desirable to generate polyploid rapeseed (Brassica napus L.) germplasm with varying flowering time controlled by a few genes. In the present study, BnaSVP, a rapeseed homolog of the Arabidopsis SVP (Short Vegetative Phase) gene, was characterized and a set of mutants was developed using a CRISPR/Cas9-based gene-editing tool. A single construct targeting multiple sites was successfully applied to precisely mutate four copies of BnaSVP. The induced mutations in these copies were stably transmitted to subsequent generations. Homozygous mutants with loss-of-function alleles and free transgenic elements were generated across the four BnaSVP homologs. All mutant T1 lines tested in two environments (summer and winter growing seasons) showed early-flowering phenotypes. The decrease in flowering time was correlated with the number of mutated BnaSVP alleles. The quadruple mutants showed the shortest flowering time, with a mean decrease of 40.6%–50.7% in length relative to the wild type under the two growth conditions. Our study demonstrates the quantitative involvement of BnaSVP copies in the regulation of flowering time and provides valuable resources for rapeseed breeding.