In G-M experiment we found that the number of counting of G-M device is different each time, under the same conditions each time of measuring as time and background counts.
You do not provide the radioisotope that you are using nor the time frame you are measuring over. There are two possible issues. First, radioactive decay is a random event. Even with a long-lived isotope, the number of counts you record in a relatively short period can be different from that of a repeated count of the same duration. You will find that the longer your counts, the more similar they will be. Second, if you have a relatively short-lived isotope, the starting activity during your second count could be considerably less than that during your first count. In other words, the activity is decaying away before you can complete your second count.
Firstly, the time is the same each time of measurement and equals 60 sec.
Secondly, How the active decay away for a radioactive source if the time of the second measurement is approximately 10 sec of the first measurement (which is the time of repeating)?
You did not specify the radioisotope you are using but I am guessing it is a long-lived one. One minute is a short count if the amount of radioactivity is relatively low. Your differing count results are probably due to the random nature of the decay event. Increase your count time. I guarantee the difference between counts will decrease.