With the advent of light and economical Unmanned Vehicles (UAVs), the Internet of Things (IoT) in air is gaining more popularity. However, IoT in air has its own set of requirements and challenges. It is unwise to upload legacy IoT applications to aerial computing networks. For instance, aerial computing in resource constraint UAVs demands energy-efficient solutions. Fortunately, mobile edge computing (MEC) can assist aerial computing by offloading partial or all applications to edge servers (ESs) in MEC. Nevertheless, ESs are subjected to finite resources, and there is a certain probability of failure, and the application in aerial computing is for high-reliability demands. Given the above issue, we investigate computation offloading for delay-sensitive applications under reliability constraints in MEC-enabled aerial computing network where the delay-sensitive applications are represented as scientific workflow applications. Technically, a two-phase reliability-aware computation offloading approach is proposed. More specifically, in the first stage, a multi-objective reliability-aware energy-efficient computation offloading strategy is proposed for the scientific workflow application. Secondly, an improved lazy shadowing scheme is proposed to enhance reliability, energy efficiency, and load balancing. Extensive experiments have been conducted to show the effectiveness and superiority of our proposed solution under different situations.