What model revolver is this?

kinda looks like a colt 1907 .38.

It appears to be a Colt Police Positive.
The Police Positive had a short frame and cylinder to use the now obsolete short .32 and .38 S&W cartridges.

The similar Police Positive Special had a longer frame and cylinder to allow chambering longer rounds like the .32-20 and .38 Special.

The Police Positive was introduced in 1907 and finally discontinued in 1947.
The one pictured would be a gun made before 1924.
Pre-war models had checkering on the cylinder release, and in 1924 Colt changed from the old molded hard rubber grips as shown in the picture and started using checkered walnut with silver Colt medallions.

So.... a Colt Police Positive made before 1924.  
Caliber would be one of the short .32 or .38 rounds.
Since Colt didn't want competitor S&W's name on Colt revolvers, Colt simply renamed the ,32 and .38 S&W cartridges with Colt names like the .32 Colt New Police and .38 Colt New Police.

Going with a 38 based on thickness of the cyl walls.

Yep, short cylinder and thin walls, .38 S&W.

.32 cylinders look like .357 N-frame cylinders, lots of meat.

That is the pistol the shot Teddy Roosevelt.

Here is mine. It was my Great Grandfathers

Yours is a Colt New Army model.
If it has US military stamps on the butt it was an official military issue revolver.
The serial number is also on the butt, in two lines.

The other numbers on parts were factory assembly numbers to keep fitted parts together during manufacture.
They ARE NOT the serial number.
All assembly numbers should match or parts have been replaced.

It's not unusual to find these with the serial number ground off the butt.  That makes the gun ILLEGAL and a felony to possess.

You can find the date made here:

http://proofhouse.com/colt/

Colt invented the modern double action swing-out cylinder revolver.  The first model was the New Navy of 1889.
The Army also bought it in 1892.
It was improved a number of times and finally discontinued in 1907.
It was the New Army Model 1896 that failed in the Moro War in the Philippines and led to the development of the .45 Automatic.

These were made as both military issue and commercial guns.
The military models had smooth walnut grips and US inspectors stamps on the frame.  Caliber was .38 Long Colt.  Barrel was 6 inches.
The commercial models had molded hard rubber grips with checkering and Colt logos, and were available in .38 Long Colt and .41 Long Colt.
Very late in production some were chambered for 32-20 and .38 Special, and different barrel lengths were available.

NOTE: The .38 Long Colt IS NOT the .38 Special and the gun should NOT be fired with ANY standard load of the .38 Special.
If you want to shoot it and it's in shooting shape you can still buy .38 Long Colt ammo from the Cowboy ammo makers, and you can hand load VERY LIGHT loads using .38 Special brass.

Also note that the New Army & Navy is a very fragile, highly complicated action that breaks or gets out of order easily.  Treat it GENTLY.

Mine does not get shot. It is a New Army. Unfortunately there is significant cylinder wobble. Probably because someone in my family shot .38 special through it. It hasn't been fired since the 60's. It now resides in a safe at my fathers house only to come out for show and tell once in a great while. The double action pull on it feels like 15 lbs.