Optical pulse shaping finds many important applications in the area of ultrafast photonics. For example, in ultrafast all-optical switching, temporal shaping of the control pulses can be used to create a wide flat-top switching window with sharp rise and fall times. Such switching windows are more jitter-tolerant than simple Gaussian windows, and can therefore achieve a lower bit-error rate. Previously reported pulse shaping methods using linearly chirped Fibre Bragg Gratings (FBGs) take advantage of the direct correspondence between the spatial distribution of the grating periods and the temporal distribution of the spectral contents of the grating impulse response (space-to-frequency-to-time mapping). However, they have two major drawbacks: first, they are only valid for high-dispersion gratings, and therefore are unsuitable for producing short pulses; second, due to the inherent impulse response assumption, the power conversion efficiency is very low since the grating bandwidth needs to be much smaller than that of the input pulse. The numerical conversion efficiency demonstrated for this method is about a few percent. We report a versatile technique for temporal pulse shaping using a simple linearly chirped FBG and an amplitude mask. Unlike previous pulse shaping methods, ours is also applicable for low-dispersion gratings with bandwidths comparable to that of the input pulse (i.e., taking into account of finite input pulse duration). The chirped grating is used to stretch the incoming pulses to the desirable temporal width, while the amplitude mask modifies the shape of the pulses. We developed a novel optimization algorithm to obtain an amplitude mask that significantly increases the conversion efficiency. Pulse shaping using linearly chirped FBGs in the low dispersion regime is simulated using two methods. For weak gratings, the direct relationship between the spatial grating profile and the grating impulse response was used in tandem with a forward-correction deconvolution algorithm to solve for the optimum amplitude mask. For strong gratings, an optimization algorithm based on the partial validity of space-time mapping, as well as the causal relationship between the reflected temporal response and the grating apodization profile was used to design the amplitude mask. We experimentally demonstrated the conversion of 1-ps transform-limited Gaussian pulses to 10-ps pulses with a target shape at a high conversion efficiency of ~20% (measured) using a 1.5-mm-long grating. The spectral width of the pulses is 3.5 nm, centered at 1.55μm. As the reflected pulse shape is controlled by the shape of the amplitude mask, our method can be easily adapted to produce any arbitrary temporal pulse shape by designing an appropriate amplitude mask. To our knowledge, this is the first demonstration of this technique of arbitrary pulse shaping using the combination of a linearly chirped fiber grating and an amplitude mask in the low-dispersion regime.