We propose an Ekblom promoting adaptive algorithm (EPAA) which uses Ekblom norm to construct a data reusing scheme to achieve better performance under impulsive noise (IN) environments. By exerting Ekblom-norm constraint on the a posterior error vector, a sliding window cost function is created to realize the EPAA that is derived to reduce IN effects. The derivation and theoretical convergence analysis of the EPAA are presented in detail. The simulation examples are setup to illustrate the superior performance of the EPAA compared to popular data reusing algorithms for system identification under IN environments.