Russ Shafer-Landau is a leading moral philosopher. Below is his case on how there can be objective morality without belief in God.
Shafer-Landua is a moral realist–he thinks that morality is real, true, binding, and he is not a moral naturalist but a moral non-naturalist. Though I am a moral naturalist, I have learned an immense amount from reading Shafer-Landau. If you want to read an introduction to moral philosophy and the contemporary debates in the field, Shafer-Landau has written a pair of books I would recommend checking out. If you want an anthology of contemporary moral philosophy with a wide array of rigorous, important essays orienting to most of the major debates, all with lucid and illuminating introductions to each major topic, Shafer-Landau coedited Blackwell’s Foundations of Ethics: An Anthology. Last but not least, if you would like something at an intermediary level of difficulty that makes a thorough and vigorous case for non-naturalistic moral realism while easily explaining and critically analyzing a number of other positions, check out Shafer-Landau’s superb Moral Realism: A Defence.