Establishing a carbon-neutral mobility is a major challenge of our time. Whereas e-mobility is important to substitute cars with combustion engines, this technology is less suitable for heavy duty mobility like trucks and ships. One sustainable alternative would be carbon-neutral liquified gas (GreenLNG) - i.e., liquified gas synthesized from renewable carbon material like waste from wood industry and produced with green energy. In our research, we wanted to predict people's acceptance of such a fuel for ship-travel and explore their willingness to pay more relative to conventional ship-travel. In two surveys in Austria (N = 725 & N = 738), we assessed several psychological variables like problem awareness, perceived outcome efficacy, social norms, and trust to predict acceptance. Even though the data did not fit the preregistered model well, results indicated that acceptance predicts willingness to pay and that the psychological variables (besides knowledge about GreenLNG) are substantially intercorrelate. After revising the hypothesized model, we collected new data in Germany (N = 415) to validate the revised model. Indices confirmed good model fit and this model indicates a central role of perceived outcome efficacy, which together with problem awareness and social norms predict acceptance. Based on these three studies, we conclude that it might be crucial to strengthen people's understanding of the beneficial consequences for the environment of carbon-neutral liquified gas as fuel in the shipping industry to increase acceptance and willingness to pay slightly higher prices for eco-friendly ship-travel.