Data　reconstruction　is　essential　in　enhancing　the　quality　of　vehicle　trajectory　data.　Previous　studies　have　identified　the　location　of　abnormal　data　inaccurately,　resulting　in　poor　trajectory　reconstruction　results.　This　study　proposed　a　two-step　reconstruction　method.　The　first　step　detected　the　locations　of　obviously　abnormal　speed　data　using　wavelet　transform.　Then,　the　abnormal　data　were　repaired　by　the　cubic　spline　curve　interpolation　algorithm.　The　second　stage　identified　the　locations　of　abnormal　acceleration　data　based　on　the　general　acceleration　value.　And　the　vehicle　trajectory　data　were　reconstructed　using　Lagrange　interpolation　and　Kalman　filter　algorithms.　The　approach　was　utilized　on　NGSIM　trajectory　data.　The　results　show　that　the　acceleration　values　of　the　proposed　method　range　from　−6.69　m/s2　to　4.96　m/s2,　with　a　standard　deviation　of　0.87.　The　reconstructed　results　are　more　closely　matching　drivers＇　physiological　capabilities　compared　to　other　methods.　These　findings　verify　the　reliability　of　the　proposed　approach　and　notably　improve　the　quality　of　the　trajectory　data.　It　provides　critical　foundational　data　support　for　traffic　planning,　design,　and　management.　©　2024　The　Author(s).　Engineering　Reports　published　by　John　Wiley　&　Sons　Ltd.