Read the sensor with SCT-013 Sensor

I am building the circuit and programming the arduino like this Learn | OpenEnergyMonitor, but it show that the current was unstable in range about 0,03 - 0,3 without connect the SCT-013 sensor to the source. What can I do to resolve it?
I’m sorry for my English

You are picking up noise. Most likely it is coming from the digital part of your Arduino via the power supply to the analogue part. There are plenty of threads about this in the Archive section. There is very little you can do to resolve the problem, but adding smoothing to the 5 V supply might help.

So I can say that there’s no problem with my circuit and my sensor, isn’t that?

Can you explain me what should I do with my 5V supply?

First, check that you read the correct current when you have a large load. You can loop the current-carrying wire through the current transformer several times to increase the sensitivity. With the wire passing through once, it will read up to 100 A, twice up to 50 A, 4 times up to 25 A, etc. Then you must change the current calibration constant to make the reading correct, from 111.1 to 55.55, 27.775, etc.
Unless you are measuring up to the full 100 A, that will reduce your spurious reading.
Remember, 0.3 A represents an inaccuracy of only 0.3% of the maximum reading.

If it is still a problem, try connecting a large electrolytic capacitor (say 220 μF or 470 μF) between GND and 5 V, but make sure you get it the right way round. It might help, but I cannot guarantee that it will.

In this case, I try to disconnect my sensor from the circuit and then the the result doesn’t change at all…
What about that?

Read again what I wrote in post 2. It is not the sensor, I think it is your Arduino.