While inversion of seismic velocity from receiver function data could be instable due to its intrinsic non-linearity and non-uniqueness, improper stacking of receiver function could also introduce significant biases to the resulting velocity structure. In a distance section of receiver functions, the Moho Ps conversion and the two reverberations possess a positive and negative moveout, respectively. Stacking receiver functions without moveout correction could significantly reduce and distort the amplitude and waveform of these phases. Inversion with these incorrectly stacked receiver functions will thus inevitably introduce artefacts to the resulting velocity structure. In this study, we have improved the inversion procedure in two ways. First, we introduce a ray-parameter based (RPB) stacking method to correctly construct receiver function data for inversion. Specifically we develop a ‘four-pin’ method that accounts for the moveout effect of the converted and reverberated phases in stacking individual receiver functions recorded at various distances. Secondly, we divide the receiver function trace into conversion and reverberation windows and assign different weights between the two windows in the inversion. More weight is given to the Ps conversion window in resolving the shallow structure, which can be nearly fixed in the successive inversion of deeper structure. We also employ other pre-conditioning proposed by previous studies, such as balancing the receiver function data being filtered with different Gaussian filters, smoothing the velocity model and further regulating the model based on existing information. We compute synthetic receiver functions at distances between 30◦ and 90◦ from a target model and then use the RPB stacking method to generate the input data for various inversions (iterative linear) with different initial models. Our inversions with enhanced pre-conditioning and RPB stacked data demonstrate a good capability in recovering the target model from generally more stable iterations. Applying these techniques to two broad-band stations in China indicates that the improvements on data stacking and inversion can eliminate potential stacking-induced artefacts, and yield models more consistent with surface geology.