Multitasking　optimization　(MTO)　is　promising　to　become　the　next-generation　mainstream　optimization　paradigm　for　optimizing　multiple　tasks　simultaneously　with　high　efficiency　and　accuracy.　However,　despite　dynamic　tasks　abound　in　the　real　world,　such　as　flow　shop　scheduling,　vehicle　routing,　IoT,　machine　learning,　research　on　dynamic　multitask　optimization　(DMTO)　has　been　rarely　reported.　DMTO　problems　are　more　challenging　than　MTO　with　static　tasks　or　a　single　dynamic　optimization.　In　this　paper,　a　dynamic　multitask　optimization　algorithm　with　an　improved　knowledge　transfer　mechanism　(IK_DMTO)　is　proposed　to　solve　the　DMTO　problems.　Firstly,　an　improved　knowledge　transfer　mechanism　is　designed　to　promote　knowledge　utilization　by　conditionally　selecting　the　scale　of　knowledge　transfer　and　reduce　negative　migration　by　selectively　performing　the　crossover　operation　between　tasks.　Secondly,　a　new　individual　information　update　strategy　is　applied　to　guide　the　individual　updates,　in　which　the　leaders　of　the　sub-populations　formed　during　the　knowledge　transfer　process　are　utilized　to　adjust　the　direction　of　individuals　to　make　the　utmost　of　knowledge　between　tasks,　and　an　external　archive　management　strategy　is　introduced　to　achieve　a　better　distribution　of　non-dominated　solutions.　Finally,　nine　dynamic　multi-objective　multitask　optimization　(DMOMTO)　problems　are　constructed　with　the　dynamic　multi-objective　benchmark　functions　to　verify　the　effectiveness　of　IK_DMTO.　The　experimental　results　show　that　IK_DMTO　can　perform　well　on　convergence　compared　to　the　comparison　algorithms.