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tokens: The Kepler Space Telescope was launched in 2009 March and its main scientific goal was to search for the terrestrial planets using the transit method (Borucki et al. 2010 ). The asteroseismology program is an extremely important byproduct of the Kepler mission (Gilliland et al. 2010 ). Due to the unprecedented photometric precision on the order of a few μ mag with a high duty-cycle, and continuous collection of data over about 4 years, Kepler data allows one to study the internal structure and physical process of stars with an ultra-high precision than that obtained with any telescope on earth (Koch et al. 2010 ). The Kepler telescope is in a 372.5 day Earth-trailing orbit and its field of view covers 105 deg 2 in the constellations of Cygnus and Lyra. Kepler provides two observation strategies for its targets, i.e., short cadence (SC) and long cadence (LC) with sampling times of 58.85 s and 29.424 minutes, respectively. The SC observations are adopted for the primary mission as they are able to obtain more data points during a candidate object passing in front of its host star. However, most of the targets are observed with LC in order to maximize the target’s number through long exposure time. Consequently, more than 170,000 targets are available in LC observations (Jenkins et al. 2010 ). More than 2000 δ Sct stars have been detected through the Kepler mission (Balona Dziembowski 2011 ; Balona 2014 ; Bowman et al. 2016 ). One of them, KIC 5950759, has been classified as a double-mode high-amplitude δ Sct (HADS) star by analyzing the LC data (Bowman et al. 2016 ). The δ Sct stars are typical A- and F-type variable stars with period from 0.02 to 0.25 days. They are usually on or above the main sequence on the H-R diagram, and are situated in the lower classical instability strip (Breger 2000 ). Their oscillations are mainly driven by the κ mechanism that occurs in the partial ionization zone of He ii (Gautschy Saio 1995 ; Breger 2000 ). The δ Sct stars can oscillate in both pressure and gravity modes (Breger 1995 , 2000 ; Balona 2016 ). As a subclass of δ Sct stars, the HADS stars usually pulsate with a light amplitude larger than 0.3 mag and generally rotate slowly with v sin i ≤ 30 km s −1 (Breger 2000 ). Compared with the low-amplitude δ Sct stars, the HADS stars possess a more restrictive instability strip with a width in temperature of about 300 K and tend to shift to a lower temperature with evolution (McNamara 2000 ). Lee et al. ( 2008 ) reveal that only about 0.24 percent of the stars suited in the δ Sct region belong to HADS stars. The majority of HADS stars are typically young and metal-rich Population I stars; some have been confirmed to be SX Phe variables, and are Population II metal-deficient stars (Breger 2000 ; Balona Nemec 2012 ). In general, the HADS stars pulsate with only one or two modes (e.g., AE UMa, Niu et al. 2017 ; YZ Boo, Yang et al. 2018 ; etc.), and most of their pulsations belong to radial modes. AI Vel (Walraven