Virtual synchronous generator (VSG) is a promising solution for inertia support of the future electricity grid to deal with the frequency stability issues caused by the high penetration of renewable generations. However, the power variation in power electronic interface converters caused by VSG emulation increases the stress on power semiconductor devices and hence has a negative impact on their reliability. Unlike existing works that only consider stability for VSG control design, this paper proposes a double-artificial neural network (ANN) based method for designing VSG inertia parameter considering simultaneously the reliability and stability. First, a representative frequency profile is generated to extract various VSG power injection profiles under different inertia values through detailed simulations. Next, a functional relationship between inertia parameter (H) and lifetime consumption (LC) of VSG is established by the proposed double-ANN reliability model: AN Nt provides fast and accurate modeling of thermal stress in the semiconductor devices from a given operating profile; With the aid of AN Nt, AN NLC is built for fast and accurate estimation of LC for different inertia parameters in the next step. The proposed approach not only provides a guideline for parameter design given a certain LC requirement, but can also be used for optimal design of VSG parameter considering reliability and other factors (e.g. inertia support in this paper). The proposed technique is applied to a grid-connected VSG system as a demonstration example.