function modify_upload_mimes ( $mimes_types ) {
    // add your extension to the mimes array as below
    $mimes_types['zip'] = 'application/zip';
    $mimes_types['gz'] = 'application/x-gzip';
    return $mimes_types;
}
add_filter( 'upload_mimes', 'modify_upload_mimes', 99 );

function add_allow_upload_extension_exception( $types, $file, $filename, $mimes ) {
    // Do basic extension validation and MIME mapping
    $wp_filetype = wp_check_filetype( $filename, $mimes );
    $ext         = $wp_filetype['ext'];
    $type        = $wp_filetype['type'];
    if( in_array( $ext, array( 'zip', 'gz' ) ) ) { // it allows zip files
        $types['ext'] = $ext;
        $types['type'] = $type;
    }
    return $types;
}
add_filter( 'wp_check_filetype_and_ext', 'add_allow_upload_extension_exception', 99, 4 );

WordPress version 4.7.1 ot greater, its added some extra security check for mime types. Just Add the follows code snippet in your active theme’s functions.php

By Sonic