You could try MonoDevelop, which is a clone of VisualStudio, but it hasn't as much features. MonoDevelop uses the Mono framework, a platform-independent implementation of C# and the CLI, but it's not fully compatible with .NET. You will have to port your .NET applications to Mono. At least you have to rewrite the UI, WPF isn't included in Mono and Winforms is crappy on Linux.
Although there are some Linux applications written in C# (Banshee, Tomboy, Pinta, PDFMod, Smuxi), .NET/Mono isn't very popular on Linux. It's not officially supported by Microsoft, and the developers of Mono (Xamarin) are actually focusing on mobile devices (Android, iOS) and not the Linux desktop. I recommend you to switch to another IDE and programming language that is fully supported on Linux. If you really can't live without .NET (e.g because you make your living writing .NET programs), you have to keep using Windows, because that's the only platform it supports.