Puede usar eventos de carrusel según el documento . Por favor, intente con el siguiente código.
var owl; $(document).ready(function(){ owl = $(".owl-carousel").owlCarousel({ autoplay: false, autoplaySpeed: 300, loop: false, navSpeed: 300, items: 1, margin: 2 }); owl.on('changed.owl.carousel', function(e) { $('#continue-btn').html('Continue ' + e.item.index); }); }); body { margin: 0; padding: 0; } .owl-carousel .item { height: 120px; background: #4DC7A0; padding: 1rem; list-style: none; margin: 10px; text-align: center; color: white; font-size: 20px; line-height: 120px; } <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script> <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/OwlCarousel2/2.1.6/assets/owl.carousel.css"> <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/OwlCarousel2/2.1.6/assets/owl.theme.default.min.css"> <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/OwlCarousel2/2.1.6/owl.carousel.min.js"></script> <div class="owl-carousel"> <div class="item"> slide1 </div> <div class="item"> slide2 </div> <div class="item"> slide3 </div> <div class="item"> slide4 </div> <div class="item"> slide5 </div> <div class="item"> slide6 </div> <div class="item"> slide7 </div> <div class="item"> slide8 </div> <div class="item"> slide9 </div> </div> <button id="continue-btn"> Continue </button>