In smart grid, usage reports of consumers are collected via the smart meters (SMs) and sent to the power management and control center. In addition, some instructions are sent from the control center to the SMs. These two‐way communications between customers and energy suppliers are subject to numerous security threats. Due to the limited processing capability and storage space of the SMs, it is required to employ lightweight communication schemes. To do so, quite recently, Liu et al have proposed an interesting lightweight authenticated communication scheme for the secure bidirectional communications of SMs and neighborhood gateways in smart grid. In this paper, we first demonstrate that their scheme suffers from the SM's memory modification attack and pollution attack, then, we propose an enhanced lightweight communication scheme that is secure against the mentioned attacks. The comparative performance analysis with recent works in this field shows that our scheme not only is more efficient in terms of computational complexity and communication cost, but also benefits from substantial reduction in the required storage space. Our realistic hardware implementation on two popular microcontrollers confirms this claim.