I thought that second transaction must wait until first is finished
Basically, this is not true. Your (or anyone's) database wouldn't be very efficient if only one person could do something with it at a time.
Why does it happen?
A SELECT query is taking shared locks on any rows it's looking at, so although it's not going to conflict with another SELECT query, it definitely will conflict with exclusive locks from a DELETE. As the SELECT query is not updating anything, it's usually going to be the one to be the deadlock victim, as it'll likely be the least expensive to rollback.
Why it happens specifically in the case you're talking about is not possible to say without further information. I'll add some links to deadlock detection at the end but I suspect this isn't the main purpose of the question so...
What to do?
It's difficult to know what the best approach is going to be for you (without a lot more information). It is possible that you should have a look at your isolation levels.
You could use READ_COMMITTED_SNAPSHOT, but this could result in further overheads, or use READ_UNCOMMITED/use a NOLOCK hint - I'm not a fan of those options usually as the data returned might not be actually what you want, but they may be suitable in your case. It's hard to say exactly what would be best, as it'll depend on a lot of different variables about your system and it's use.
Best thing you can do in that regard though is read up about isolation levels, these are some similar posts/sources that will start you off and go into things in more detail.
MSDN - How can a select statement result in being chosen as deadlock victim?, SQL Server central , MSDN - Understanding Isolation Levels
Don't rush to make a change just so you can get your queries to finish. A more appropriate avenue to explore may be your queries themselves.
Why is the SELECT statement taking so long to run? Why are things being deleted from the table so frequently? Maybe some simple query tuning will get them all to complete quicker and reduce the chance of a deadlock. Perhaps you need to do some general performance tuning on your database server (I won't go into detail on this here though as it's getting way off topic).
You've got to make sure your queries are fit for business purposes, rather than queries just 'completing at all costs', databases are a business tool first a foremost and need to work around that (however much we might not like that)!
Just going ahead and changing the isolation level, or even just using NOLOCK, can have big impacts on your database and also what exact results queries return - which could have business impacts.
To aid in deadlock detection, have a look at this post on StackOverflow and check out the Deadlock Information Tools on the MSDN site which will explain how to use trace flags to provide more information about your deadlocks.
More specific advice can be offered if you put the SQL Server version in your post, and some more details about what exactly the SELECT query is (to see if there's anything that may be causing it to take so long and be open for being locked).