Interval-valued　data　have　become　popular　in　many　research　areas.　Several　scholars　have　examined　regression　models　based　on　the　center　and　range　method　(CRM)　for　interval-valued　data.　However,　few　works　considered　making　probabilistic　assumptions　about　the　residuals　of　the　model.　In　this　paper,　an　interval-valued　linear　regression　model　based　on　asymmetric　Laplace　distribution　(AL-CCRM)　is　proposed.　To　fit　the　new　linear　regression　model,　the　center　and　range　of　intervals　are　both　used,　it　assumes　that　the　residuals　of　the　center　model　obey　an　asymmetric　Laplace　distribution,　and　adds　constraints　so　that　the　range　of　the　predicted　interval　variable　is　nonnegative.　AL-CCRM　is　demonstrated　to　be　useful　in　experiments　involving　both　simulated　and　real　interval-valued　data　sets.