In the last few decades, the statistical delay- bounded quality-of-service (QoS) technique has been proposed and investigated to support the delay-bounded 5G multimedia wireless services In addition, the energy harvesting (EH) based systems, which enable the mobile devices to harvest energy from various external sources, have been designed to address the energy scarcity problem. Researchers have recently integrated EH based systems with short-packet communications for their potential benefits of small payloads and low latency to support reliable multimedia data transmissions. Under the short delay requirements for the low-latency 5G multimedia wireless services, it is not ideal to apply the traditional Shannon capacity for modeling the data rate under the error-rate bounded in the non- asymptotic regime. Accordingly, researchers have developed the finite wireless data transmission rate in the non-asymptotic regime. However, it is challenging to determine the convexity of the effective-capacity maximization problem subject to the statistical delay-bounded and error-rate bounded QoS constraints due to the complexity of analyzing the maximization problem in the non- asymptotic regime. To overcome these challenges, we design the EH based cross- layer optimization scheme in supporting the statistical delay-bounded and error-rate bounded QoS requirements in the finite blocklength regime in the following steps. First, we characterize the EH based system models under finite blocklength coding (FBC). Second, we derive and analyze the convexity of the /spl epsilon/-effective capacity maximization problem for our proposed EH scheme in the finite blocklength regime. Finally, we conduct several simulation evaluations which validate our proposed EH scheme under the statistical delaybounded and error-rate bounded QoS constraints in the finite blocklength regime.