看一下注释，这个文件一般是由其它工具生成的；例如：resolv-conf，network-manager，systemd-resolvd。你需要根据提示修改对应工具的配置文件才可以。例如我的一台 Ubuntu 机器上的 /etc/resolv.conf：

# This file is managed by man:systemd-resolved(8). Do not edit.
#
# This is a dynamic resolv.conf file for connecting local clients directly to
# all known uplink DNS servers. This file lists all configured search domains.
#
# Third party programs must not access this file directly, but only through the
# symlink at /etc/resolv.conf. To manage man:resolv.conf(5) in a different way,
# replace this symlink by a static file or a different symlink.
#
# See man:systemd-resolved.service(8) for details about the supported modes of
# operation for /etc/resolv.conf.

nameserver 8.8.8.8
nameserver 192.168.88.1

This file is managed by man:systemd-resolved(8). Do not edit.

分享：如何在 Ubuntu 16 中修改 DNS 服务器？

感谢楼上两位老哥的讲解