I want to check the SMS delivery status in journey builder to take further action based on the status.
Is there any way to check delivery status in the journey itself?
There isn't away to check the delivery status of SMS in Journey Builder itself. But there is a new data view that may be useful to you for this:
https://help.salesforce.com/articleView?id=mc_as_data_view_sms_message_tracking.htm&type=5
You could query this and update the DE with the info you are looking for.