Constrained　multitask　optimization　(CMTO)　problems　are　frequently　encountered　in　practical　applications.　However,　since　the　feasible　regions　of　different　tasks　are　difficult　to　match　under　constraints,　it　is　hard　to　obtain　and　transfer　effective　knowledge　among　different　tasks,　resulting　in　poor　convergence　performance.　To　address　this　issue,　a　constrained　multitask　particle　swarm　optimization　algorithm　with　knowledge　transfer-based　adaptive　penalty　function　(CMTPSO-APF)　is　proposed　to　improve　the　convergence　performance.　The　main　contributions　of　CMTPSO-APF　are　three-fold.　First,　a　dynamic　particle　topology　is　designed　to　improve　the　neighborhood　similarity　for　different　tasks　with　constrained　conditions.　Then,　the　particles　with　similar　spatial　structures　can　facilitate　the　knowledge　transfer　between　different　tasks.　Second,　a　covariance　matrix　learning　mechanism　is　proposed　to　obtain　valid　knowledge　with　constrained　conditions.　Then,　the　proposed　method　can　promote　the　population　to　move　in　the　direction　of　the　optimal　solution.　Third,　a　knowledge　transfer-based　adaptive　penalty　function　for　constrained　multitask　optimization　is　designed　to　achieve　the　dynamical　change　of　penalty　factor　according　to　the　evolution　state.　Then,　the　adaptive　penalty　function　can　promote　the　transfer　of　effective　knowledge　and　improve　the　convergence.　Finally,　some　simulation　experiments　are　carried　out　on　the　CMTO　benchmark　test　suites　and　the　practical　application　of　the　wastewater　treatment　process.　The　results　indicate　that　CMTPSO-APF　can　improve　the　convergence　performance.