Conversion from neutron stars to strange stars as a possible mechanism of cosmological gamma-ray bursts ( GRBs ) has been discussed in previous works , although the existence of strange stars is still an open question . On the basis of this mechanism , we here outline an explanation of the connection between supernovae ( SNe ) and GRBs , which has got increasing evidence recently . An asymmetric but normal SN explosion leaves a massive ( \geq 1.8 { M _ { \odot } } ) and rapidly rotating neutron star , which then converts to a strange star few days later , due to its rapid spindown . The accompanied fireball , which can be accelerated to ultra-relativistic velocity ( \Gamma _ { 0 } \sim 100 ) due to the very low baryon contamination of the strange star , flows out along the direction of the high-velocity SN jet and subsequently produces a GRB and the following low energy afterglows by interacting with the surrounding stellar wind . We will also expect a very luminous supernova like SN1998bw , if a large fraction of the conversion energy finally turns into the kinetic energy of the supernova ejecta .