By default, TabControl doesn't support the close button, to create TabControl with the close button, you can modify your code as shown below.
Creating a new Windows Forms Application project, then open your form designer.
How to Add a close button to Tabs in TabControl c#
Dragging TabControl from your Visual Studio Toolbox to your form designer.

Right-clicking on the TabControl, then select Properties. Next, you need to set the DrawMode of your TabControl to OwnerDrawFixed.
Opening your code behind, then declare as shown below.
Point _imageLocation = new Point(20, 4);
Point _imgHitArea = new Point(20, 4);
Image closeImage;
Right-clicking on your project, then select Properties => Resources. Next, Copy a close button image (16x16) into the Resources tab.

Adding a Form_Load event handler to your form allows you to initialize a close button with TabControl.
private void Form1_Load(object sender, EventArgs e)
{
closeImage = Properties.Resources.close;
tabControl1.Padding = new Point(20, 4);
}
Adding a Draw_Item event handler to the TabControl allows you to draw image close button to the TabPages.
private void tabControl1_DrawItem(object sender, DrawItemEventArgs e)
{
Image img = new Bitmap(closeImage);
Rectangle r = e.Bounds;
r = this.tabControl1.GetTabRect(e.Index);
r.Offset(2, 2);
Brush TitleBrush = new SolidBrush(Color.Black);
Font f = this.Font;
string title = this.tabControl1.TabPages[e.Index].Text;
e.Graphics.DrawString(title, f, TitleBrush, new PointF(r.X, r.Y));
e.Graphics.DrawImage(img, new Point(r.X + (this.tabControl1.GetTabRect(e.Index).Width - _imageLocation.X), _imageLocation.Y));
}
Adding a Mouse_Click event handler to the TabControl allows you to remove TabPage.
private void tabControl1_MouseClick(object sender, MouseEventArgs e)
{
TabControl tabControl = (TabControl)sender;
Point p = e.Location;
int _tabWidth = 0;
_tabWidth = this.tabControl1.GetTabRect(tabControl.SelectedIndex).Width - (_imgHitArea.X);
Rectangle r = this.tabControl1.GetTabRect(tabControl.SelectedIndex);
r.Offset(_tabWidth, _imgHitArea.Y);
r.Width = 16;
r.Height = 16;
if (tabControl1.SelectedIndex >= 1)
{
if (r.Contains(p))
{
TabPage tabPage = (TabPage)tabControl.TabPages[tabControl.SelectedIndex];
tabControl.TabPages.Remove(tabPage);
}
}
}
Through this c# example, i hope so you can easily create c# close tabs for TabControl.