Active polymers are slender or chain-like self-propelled objects. Synthetic chains of self-propelled colloidal particles are one of the examples, which provide a potential way to develop varied active polymers. Here, we study the configuration and dynamics of an active diblock copolymer chain. Our focus is on the competition and the cooperation between the equilibrium self-assembly due to chain heterogeneity and the dynamic self-assembly due to propulsion. Simulations show that an active diblock copolymer chain can form the spiral(+)/tadpole(+) states under forward propulsion and the spiral(-)/tadpole(-)/bean states under backward propulsion. Interestingly, it is easier for the backward-propelled chain to form a spiral. The transitions between the states can be analyzed in terms of work and energy. For forward propulsion, we found a key quantity, i.e. the chirality of the packed self-attractive A block, which determines the configuration of the whole chain and the dynamics. However, no such quantity is found for the backward propulsion. Our results set the foundation for further study of the self-assembly of multiple active copolymer chains and provide a reference for the design and application of polymeric active materials.