Solution
The error message is showing that you do not have permission to access yourdb.ns database. Check the MongoDB data directory /data/db/ , the database yourdb.ns belongs to the root user.
$ ls -ls /data/db
0 drwxr-xr-x 2 mkyong wheel 68 Mar 8 22:54 journal
131072 -rw------- 1 root wheel 67108864 Mar 7 17:01 yourdb.0
262144 -rw------- 1 root wheel 134217728 Mar 7 16:15 yourdb.1
32768 -rw------- 1 root wheel 16777216 Mar 7 17:01 yourdb.ns
$whoami
mkyong
To fix it, assign permission to the database.
$ sudo chown -R mkyong /data/db
$ ls -ls /data/db
0 drwxr-xr-x 2 mkyong wheel 68 Mar 8 22:54 journal
131072 -rw------- 1 mkyong wheel 67108864 Mar 7 17:01 yourdb.0
262144 -rw------- 1 mkyong wheel 134217728 Mar 7 16:15 yourdb.1
32768 -rw------- 1 mkyong wheel 16777216 Mar 7 17:01 yourdb.ns
转自：
http://www.mkyong.com/mongodb/mongodb-couldnt-open-datadbyourdb-ns-errno13-permission-denied/
MongoDB : couldn’t open /data/db/yourdb.ns errno:13 Permission denied
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