Is it possible to compress random sequence with high entropy I have an algorithm that generates pseudo random sequence with length of 100k and high entropy. I would like to check the quality of randomness. So, I used a popular software to compress the generated file and it could manage to compress the original file into a file with just one-third of original file.
I have come across to some random test suites out there. But, I have no idea why a random sequence with high capacity can be compressed like this.

My question is whether compressing the generated file is a proper test?
Does the algorithm fail because of the generated file can be compressed?

Any comment is appreciated.
Random data can not be compressed. Good pseudo random data can not be compressed(with generic algorithm). 
As Paul commented if you use an inefficient encoding such as hexadecimal or Decimal ASCII characters you are using a full 8 bit character to represent less information. Hexadecimal is compressible to 50% and decimal to $\log_2(10)/8$ which is approx 41%.
If your data is in binary or compresses significantly more than the inherit encoding used.  This is a significant flaw in your random number generator.
A compression test with a Lempel-Ziv based compression algorithm is a good important but not sufficient test. It essentially tests for repeating sequences of arbitrary length. So it can find all sorts of biases in your algorithm.

However for cryptographic security, the chances your homegrown algorithm is secure are slim even it passes all generic statistical tests with flying color.