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We investigate the fishtail effect, critical current density (Jc) and vortex dynamics in LiFeAs single crystals. The sample exhibits a second peak (SP) in the magnetization loop only with the field || c-axis. We calculate a reasonably high Jc, however, values are lower than in 'Ba-122' and '1111'-type FeAs-compounds. Magnetic relaxation data imply a strong pinning which appears not to be due to conventional defects. Instead, its behavior is similar to that of the triplet superconductor Sr2RuO4. Our data suggest that the origin of the SP may be related to a vortex lattice phase transition. We have constructed the vortex phase diagram for LiFeAs on the field-temperature plane.PACS numbers: 74.25. Ha, 74.25.Sv, 74.25.Wx The fishtail effect or the anomalous second peak (SP) in field (H) dependent magnetization (M ) loops has been a subject of intense research topic in the field of superconductors with both low and high transition temperatures (T C ).1-13 This phenomenon is realized with the enhanced irreversibility in isothermal M (H) or, equivalently, the enhanced critical current density (J c ) at high fields apart from the central peak which occurs around zero field. In type-II superconductors, the magnetic fields above the lower critical field (H c1 ) penetrate the bulk of the sample in the form of flux lines or vortices. Different mechanisms based on the vortex dynamics have been discussed to explain the SP in high-T C cuprates which include inhomogeneity of the sample, 2,3 matching effect, vortex order-disorder phase transition, 9-12 crossover from elastic to plastic creep, 13 etc. However, in spite of plenty of studies dealing with this phenomenon, the general understanding lacks a converging trend and the proposed models appear to be more sample specific.The recent discovery of superconductivity (SC) in Febased pnictides 14 has renewed the interest in vortex dynamics. Similar to cuprates, pnictides are also layerbased superconductors, and exhibit a high T C and type-II nature. In contrast, pnictides have less anisotropy and larger coherence length (ξ), thus raising question how these influence the vortex dynamics in these materials. The appearance of a SP in M (H) is not an universal phenomenon in different families of pnictides. For the '122' family (AFe 2 As 2 , A = Ba, Sr, Ca, etc.) the appearance of a SP is sensitive enough to the compositional elements. The pronounced SP has been observed, for example, in both hole-and electron-doped Ba-122 compounds, which has been ascribed to various mechanisms, 15-21 but it remains absent in doped Ca-122 compounds.22 Similarly, a SP is not consistently seen in the '1111' (REFeAsO, RE = La, Nd, Ce, Sm, etc.) and in the '11' (FeTe) families. 23-25However, to the best of our knowledge the vortex dynamics have not been studied in the '111' family (AFeAs, A = Li, Na, etc) up to now.Here we study the fishtail effect and the vortex dynamics in single crystals of LiFeAs which belong to the 111 family of pnictides. LiFeAs is an oxygen free compound where superconducting ...