Pollution, congestion and urbanistic considerations are leading to a change in the use of private vehicles in dense city centers. More frequently, the last-mile is covered with systems such as public transport, car sharing and bike sharing as well as an increase in walking and cycling. Following this trend, we assume a hypothetical scenario where the use of private cars is strongly limited in dense urban areas, and innovative transport modes must be used. This work investigates a futuristic system based on a network of accelerating moving walkways (AMW) to facilitate the movement of pedestrians in city centers where cars have been banned. Unlike constant speed moving walkways, AMWs can reach speeds of up to 15km/h thanks to an acceleration section. This paper presents a rigorous description of the system characteristics from a transportation point of view, develops a heuristic algorithm for the network design problem, and tests it on a real case study. Given a network of urban roads and an origin-destination demand, the optimization algorithm, which combines traffic assignment and supply modification, explores the trade-off curve between the total travel time and capital cost of the infrastructure. The results give practical insight on the possible dimensioning of the system, show the optimal network designs, and how these vary with a reduction of the available budget. This paper investigates for the first time the use of AMWs at a network scale, and provides results useful for analyzing the system feasibility. The results on travel time, investment budget and payback period indicates that AMWs could be an effective mode of transport in cities.