Non-real-time (NRT) services such as nrt-VBR, ABR and UBR traffic are intended for data applications. Although NRT services do not have stringent QoS requirements for cell transfer delay and cell delay variation, ATM networks should provide NRT services while considering other criteria to ensure an excellent performance such as cell loss ratio (CLR), buffer size requirement and service fairness. Service fairness means that networks should treat all connections fairly. That is, connections with low arrival rates should not be discriminated against. In addition, given a fixed buffer size for a connection, reducing the maximum number of cells in a buffer during the lifetime of a connection can lead to a low CLR due to buffer overflow. Thus, these criteria should be considered as much as possible when designing a cell scheduler to provide NRT services. Whereas most of the conventional cell scheduling schemes are usually appropriate for one performance criterion, but inappropriate for another one. In this work, we present a novel cell scheduling scheme, called buffer minimized and service fairness (BMSF), to schedule NRT services in ATM networks. Using probability constraints and selecting a connection with the longest buffer size to transmit first allow BMSF to attain a satisfactory performance with respect to maximum buffer size requirement, CLR, and service fairness in terms of the maximum buffer size and cell waiting delay criteria. Simulation results demonstrate that BMSF performs better than some conventional schemes in terms of these criteria, particularly when NRT services have diverse arrival rates. Thus, the BMSF scheme proposed herein can feasibly schedule NRT services in ATM networks.