Occurrence of shear-induced structure, SIS, of a wormlike micelles solution on accelerated shear flow was investigated. Shear rate applied to the solution is increased from zero to a certain value linearly. In case of a step shear, this solution exhibits SIS at 4.0s^<-1> in shear rate. However, SIS does not occur when the shear acceleration is 0.1s^<-2> and shear rate is reached to 50s^<-1>. When the shear acceleration is higher than 0.4s^<-2>, SIS is generated and viscosity increased. The maximum viscosity on SIS is increased with increasing the shear acceleration until 1.5s^<-2> and it reaches a constant value.