Your soil might have too much nitrogen and not enough potassium. Try growing in a soil which has less compost(which is rich in nitrogen) in it. This is not an uncommon problem which is remedied by lowering nitrogen levels.

How deep does it go, ie is it still there on the lower layers?
If not just avoid the brown bits. the
rest will be perfectly edible. I have checked what books I have and there was nothing like that. I'm sure i've had similar in the past. If you do find out it is a deficiency it won 't affect the edibility

Refer to Goy member Newtonhurst similar question posted on Nov 22, 2011 with responses.

He suggests potash but I would have thought it would encourage them to run to flowering to soon? Anyway its too late to do anything this year.

Dear Loosestrife2,
Many thanks for your advice, As you suggest, my soil contain much compost. I will try to grow leek in soil to reduce nitrogen and add some potassium next season.

How do you say this symptom in your country?
Leek rust???

Dear Steragram,
Many thanks for your advice and sharing your experience, I was really relieved to hear that you had the similar symptom in your field. I know it is no problem to eat, but some of consumers point out that quality.
How did you cope with this symptom???

Leek rust is a name which may be applied here by some people but in your problem it is used incorrectly. Leek rust refers to a problem caused by a fungus which looks similar. Your leeks appear this way because of a “nutrient imbalance” not a fungus attack. For home consumption this appearance is not a problem. For meal presentation in a commercial setting (restaurant) this may be a problem which some customers will find unacceptable no matter what the explanation or apology. That’s the way some people are unfortunately. So the proper term is in your case is ....nutrient imbalance.....

Dear Loosestrife2,

Thanks a lot for your additional comments in detail, I clearly understood what you said.
As you know, this is serious for me. And other close farmers also have the similar symptom, I guess this region has much nitrogen.

I want to give you heartfelt thanks for what you did.

Here in the USA we have what are known as Agricultural Extension Agencies which have connections to institutions of higher learning and government. The representatives of these agencies are there to help those who grow crops from the smallest allotment to the largest farms and give advice and recommendations regarding problems such as yours. I’m sure that there are agricultural extension agencies in Japan willing to help you on a local level even at no cost. Try using your search engine to find and contact one in the area in which you live.

Dear Loosestrife2,

Thanks a lot for your advice!!
Anyway, I am very relieved to hear that the same symptom was founded in US as well.

I appreciate your supports to me, thanks.