Well the short answer is you can't. According to the Australian Stock Exchange website:
"All shares listed on ASX can only be bought or sold through a broker. A stockbroker acts as your agent to buy or sell shares on your behalf, for which a fee is charged."
This statement is clear and unambiguous. However, it got me thinking. There are actually a few exceptions to this rule. The exceptions are all share purchase transactions in which the ASX is not directly involved.
So The Long Answer Is Yes ... But In Very Limited Circumstances
There are a number a scenarios where you can buy shares without paying a stock broker. But just because you can, it doesn't mean you should. But more on that later.
Dividend Reinvestment Plans
The first option is available to investors in companies which operate a dividend reinvestment plan (or DRP).
Under a DRP, an investor is able to forgo their cash dividend and instead receive new shares to the same value. As an added bonus, some dividend reinvestment plans issue these shares at a discount to the prevailing market price.
So if you're an existing shareholder of a particular company and you'd like to increase your investment in that company, this can be an effective way of doing it without paying brokerage. Just be aware that not all companies operate DRPs.
Read more in what are dividend reinvestment plans.
Share Purchase Plans
Share purchase plans offer you another way to increase your existing shareholdings without paying a broker.
Under a share purchase plan (SPP) a company's existing shareholders are invited to buy more shares, normally at a discount to the current share price. Just like DRPs discussed above, there is no brokerage or other commissions payable on the share purchase as you are transacting directly with the company.
However, also like DRPs, you need to be an existing shareholder of the company.
Rights issues are similar to share purchase plans in that you can buy additional shares in a company without paying any brokerage. The main difference to a SPP is that under a rights issue, the number of shares you're entitled to is in proportion to your current shareholding, whereas with a SPP this is not the case.
When a company first lists on the Australian Stock Exchange, they normally offer shares to the public as a way of raising capital. Once again, since you are transacting directly with the company you will pay no brokerage.
If you are interested, here is a list of upcoming share market floats.
Saving A Little Could Cost You A Lot
As I said at the beginning of this article, I don't believe that saving money on brokerage fees should be a primary factor in your decision of which shares to buy. Saving $20 or so in stock broker's fees may turn out to be false economy if the underlying investment does poorly.
What do I mean? Well, each of the cases I've described above are very specific and somewhat opportunistic. If it were me constructing a share portfolio, I wouldn't be restricting my purchases to DRPs, SPPs, rights issues and new floats. I'd be looking for companies trading at attractive prices at the time I was ready to purchase.
So there is your long answer. You can buy shares without a broker. But not just any shares and not all of the time.
Read more about how to buy shares.