Infrared dark clouds are ideal laboratories for studying the initial processes of high-mass star and star-cluster formation. We investigated the star formation activity of an unexplored filamentary dark cloud (size ∼5.7 pc × 1.9 pc), which itself is part of a large filament (∼20 pc) located in the S254-S258 OB complex at a distance of 2.5 kpc. Using Multi-band Imaging Photometer (MIPS) Spitzer 24 μm data, we uncovered 49 sources with signal-to-noise ratios greater than 5. We identified 45 sources as candidate young stellar objects (YSOs) of Class I, flat-spectrum, and Class II natures. Additional 17 candidate YSOs (9 Class I and 8 Class II) are also identified using JHK and Wide-field Infrared Survey Explorer (WISE) photometry. We find that the protostar-to-Class II sources ratio (∼2) and the protostar fraction (∼70%) of the region are high. Comparison of the protostar fraction to other young clusters suggests that the star formation in the dark cloud possibly started only 1 Myr ago. Combining the near-infrared photometry of the YSO candidates with the theoretical evolutionary models, we infer that most of the candidate YSOs formed in the dark cloud are low-mass (<2 M ). We examine the spatial distribution of the YSOs and find that majority of them are linearly aligned along the highest column density line (N(H 2 ) ∼ 1 × 10 22 cm −2 ) of the dark cloud along its long axis at the mean nearest-neighbour separation of ∼0.2 pc. Using the observed properties of the YSOs, physical conditions of the cloud and a simple cylindrical model, we explore the possible star formation process of this filamentary dark cloud and suggest that gravitational fragmentation within the filament should have played a dominant role in the formation of the YSOs. From the total mass of the YSOs, the gaseous mass associated with the dark cloud, and the surrounding environment, we infer that the region is presently forming stars at an efficiency of ∼3% and a rate ∼30 M Myr −1 , and it may emerge in a richer cluster.