I need to display home link (parent site) in breadcrumb when I am in sub site page.
I can only see the home link when I am in same site. When I go to the sub-site, it is showing from sub-site name. I can't display the home link.
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If you are referring to the site logo that you can click on in SharePoint that takes you back to the home page, what you are describing is the default behavior. The logo always takes you back to the home page of the current site that you are in. You can quickly and easily change this by editing the master page. By default the link is set to take you to the "site" and you modify it to instead take you to "sitecollection", which will point to the top level site in the site collection.
If you are referring to the top navigation bar, you can add a new navigation item that points to the top level site home page.
If you are referring to breadcrumb navigation, for example "Home > Sub Site > Page in Sub Site", you need to activate the breadcrumb by editing the master page and adding it back in, assuming you are working with SharePoint 2013+. The breadcrumb is hidden by default starting in SharePoint 2013. Once you add the breadcrumb back in, you have to make some decisions about what you want to display in the breadcrumb navigation as there are some differences for publishing vs. non-publishing sites. I discuss how to add the breadcrumb and navigation options in detail in this blog post: https://blog.sharepointexperience.com/2015/08/31/sharepoint-2013-breadcrumb/