Make sure there's enough free space on the startup disk to install updates.
Right or control click the MacintoshHD icon on your desktop then click Get Info.
Look for Capacity and Available in the Get Info panel.
Make sure there's at least 15% available disk space.
And make sure you are logged into the admin account when running Software Update.
If there's enough free storage space and you are logged in as the admin, could be corrupted preferences.
Open the Finder. From the Finder menu bar click Go > Go to Folder
Type or copy/paste: /Library/Preferences
Click Go then move the com.apple.SoftwareUpdate.plist file from the Preferences folder to the Trash. Empty the Trash.
Then click your Apple menu > Software Update