laravel vuejs assets()

//Inside the head section of the layout create a global reference
//to the base asset path, something like this

window._asset = '{{ asset('') }}';
//Next step is to create a Vue mixin. In my case, a trans.js file with the following content:

module.exports = {
    methods: {
        asset(path) {
            var base_path = window._asset || '';
            return base_path + path;
        }
    }
}

//Make sure you include it after Vue, for example:

window.Vue = require('vue');
Vue.mixin(require('./asset'));
//and then you can use it inside all your Vue components.
//Your original code would look like this

<img :src="asset('admin/images/users/avatar-1.jpg')" width="35 px" height="23px">
//Note the lack of {{ and the addition of : in this case,
//since it is used as an attribute value.