Mormons believe in grace — as a subsequent to the exhaustion of your own good works. Yet, this is not the Biblical concept of grace; the unmerited favor of God. Grace is central to the Christian gospel, but is more of an attachment to the Mormon teaching.
For example, in the Book of Mormon, in 2 Nephi 25:23, it says,
“For we labor diligently to write, to persuade our children, and also our brethren, to believe in Christ, and to be reconciled to God; for we know that it is by grace that we are saved, after all we can do.”
In my experience, trying to talk about salvation (or exaltation, in the LDS mind) with a Mormon usually grinds down to a point where the Mormon begins pressing a Christian about grace.
Often they bring up the concept of grace, (which in the LDS mind is conditional: See this excellent article from Mormonism Research Ministry to see why) in the same way that other cultic groups use the virtue of humility in conversation.
I've seen this in action. A cult leader asks a follower why he or she won't submit and says it's a lack of humility. How do you answer such a thing? By saying, “I beg your pardon, I am very humble”?
In the same way, I have found that Mormons use “grace” as a tool when they really don't believe it in themselves. The concept is precious to us, but not so much to them, and they know it.
Read more about how that plays out in the life of faithful Mormons struggling with their religion in Latter-day Cipher and in the best-seller non-fiction, The Mormon Mirage 3rd Edition: A Former Member Looks at the Mormon Church Today(Zondervan, 2009). Also available as an audiobook and as an expanded-text E-book for Nook, Kindle and other reading devices.