You can not use kafka without zookeeper. The reasons behind this is given below.
Mainly zookeeper is used to manage all the brokers. These brokers are responsible for maintaining the leader/follower relationship for all the partitions in kafka cluster. Whenever problem occurs and nodes shut down, it is the controller from the broker that tells other replicas to become partition leaders to replace the partition leaders on the node that is going away. So zookeeper is used to elect one controller from the brokers.
Zookeeper also manages the status of the brokers, which broker is alive or dead.
Zookeeper also manages all the topics configuration, which topic contains which partitions etc.
Hope this will clear your doubt.