You have to implement ConvertTo with an int type as input (and an implicit string type as output, since you're talking to the property grid).

Also, if you want to support direct end user int input, you need also to implement ConvertFrom from an int as a string (like "2" for example).

Here is a piece of code that seems to work:

public class MyClassConverter : TypeConverter
{
    private List<string> values = new List<string>();

    public MyClassConverter()
    {
        values.Add("Value1");
        values.Add("Value2");
        values.Add("Value3");
    }

    public override object ConvertTo(ITypeDescriptorContext context, CultureInfo culture, object value, Type destinationType)
    {
        if (value is int)
        {
            int index = (int)value;
            if (index >= 0 && index < values.Count)
                return values[index];

            return values[0]; // error, go back to first
        }
        return value;
    }

    public override bool CanConvertFrom(ITypeDescriptorContext context, Type sourceType)
    {
        return sourceType == typeof(string) || base.CanConvertFrom(context, sourceType);
    }

    public override object ConvertFrom(ITypeDescriptorContext context, CultureInfo culture, object value)
    {
        string s = value as string;
        if (s != null)
        {
            int index = values.IndexOf(s);
            if (index >= 0)
                return index;

            // support direct integer input & validate
            if (int.TryParse(s, out index) && index >= 0 && index < values.Count)
                return index;

            return 0; // error, go back to first
        }

        return base.ConvertFrom(context, culture, value);
    }

    public override StandardValuesCollection GetStandardValues(ITypeDescriptorContext context)
    {
        return new StandardValuesCollection(values);
    }

    public override bool GetStandardValuesSupported(ITypeDescriptorContext context)
    {
        return true;
    }
}